How to Do Combinations: A GRE and GMAT Introduction by Top-Score Tutor

Understanding combinations can seem overwhelming for many students. But, luckily, I am here to show you that they really aren’t that bad, and before you know it you will be finding combinations like it’s no-one’s business!
I offer private GRE / GMAT tutoring online at a fixed rate of $140/hr. Please get in touch via the email below, or through my tutoring website: www.gretutorlondon.com/
Enquiries: [e-mail]
How might you be asked to count combinations? Well, a typical situation is this:
There are 8 employees in a team, and 3 of the employees are going to be promoted. In how many different ways can this be done?
Without some combinations knowledge, we are a little bit, how-to-say, royally screwed [sound effect]. We would have to list out the people, say A to H, and then find different groups of three until we think we have exhausted all the ways. Way too long! So, instead, mathematicians came up with a great time-saving formula:
n!/(n-r)!r!
I could give a bit more background to the origin of this formula if people ask for it in the comments below, but suffice to say if you know how to use it you will be greatly advantaged.
So, what does the n and r stand for, and what’s with the exclamation marks?
The n stands for the total from which we are picking out a group. It is always the biggest number. If you are selecting a group of 3 people from 8 people, 8 would be the n.
The r stands for the size of the group that you are picking out/selecting from the total. If you are selecting a team of 4 from a list of 9, the 4 would be your r.
The exclamation marks (‘!’) mean factorial. You multiply all the integers from 1 until you get to the number next to the exclamation mark. So, 5! = 5x4x3x2x1.
I will be doing another video on factorials specifically, but for the purposes of this formula, we just need to know that’s how they work.
I know you might think that the n - r and the r bit at the bottom is hard to remember, but an easy way to remember it is that the two terms on the bottom must add up to the term on the top. For example, with selecting 4 people from 9, we would have 4 and 5 factorial on the bottom and 9 factorial on top.
And when do we use this amazing formula? Whenever you need to know how many arrangements or combinations there are of doing something, when writing them all out would take too long.
You may have heard of another formula for ‘permutations’, which I will cover in another video, and wonder when to use the above combinations formula. The formula above is relevant for over 90% of the arrangement questions on the GRE and GMAT - it is by far the most important formula. To cut a long story short, we use it whenever the order of the people being selected does not matter.
Going back to our question, it does not matter if we promote persons BCD or CBD, we end up promoting the same three people.
Enough build-up, let’s use our incredible formula to answer our question!
The question shown is a classic combinations question. We don’t care about order, we just want to find all the ways of picking 3 people from a group of 8. If you want you can pause the video to see if you can use the formula yourself:
Here, n is the total, which is 8, and r is 3:
n!/(n-r)!r!= 8!/(8-3)!3!= 8!/5!3!=
8x7x6x5x4x3x2x1/((5x4x3x2x1)(3x2x1))= 8x7x6x5x4x3x2x1/((5x4x3x2x1)(3x2x1))
= 8x7x6/((3x2x1) ) = 8x7/1 = 56.
Notice how much always cancels out with factorials!
Isn’t this so exciting? We have saved so much time and got the right answer. If this is starting to make sense do hit the like button and subscribe! Also, do comment down below with any gratitude or any questions you may have.
Before you go, let me give you one more example of this core technique, just to bed it in.
Imagine there are 6 women and 5 men just chilling out relaxing, having some fun. We want to select 2 women and 2 men for a neighbourhood event.
How many ways are there of selecting 2 women and 2 men from the 11 people available?
Pause the video and have a go if you wish. Otherwise, listen-up.
First, we pick the women. Do not lump everyone together, we have to do things step-by-step!
There are 6 women available and we are picking 2. Our n is 6 and our r is 2:
n!/(n-r)!r!= 6!/(6-2)!2!= 6!/4!2!
= 6x5x4x3x2x1/((4x3x2x1)(2x1))= 6x5/2x1=15
n!/(n-r)!r!= 5!/(5-2)!2!= 5!/3!2!
= 5x4x3x2x1/((3x2x1)(2x1))= 5x4/2x1=10
Finally, what do we do with these two results - 15 selections possible of women, 10 selections possible with men?
Well, given that we want 2 women AND 2 men, we multiply the 15 and 10 to get 150 total possibilities. AND always means multiply in probability and combinations.
There are 150 (15 x 10) ways we can select a team of 2 women and 2 men from 6 women and 5 men.
I offer private GRE / GMAT tutoring online at a fixed rate of $140/hr. Please get in touch via the email below, or through my tutoring website: www.gretutorlondon.com/
Enquiries: [e-mail]

[@BeckyThatCrazyLlama]

This video is almost 3 years old now and it just completely taught me something I had written off as "too confusing." Thank you!!

[@blessyjebaraj8066]

It's been a decade and a half since I passed high school and am taking the GRE on a whim! but I never expected to enjoy the process and doing math SOOO much! thanks to this channel and the calming energy in which the tutor teaches. Sort of rekindled my love for math.

[@TheTestedTutor]

Wow thank you Blessy, I am so glad

[@angel_accel]

one of my biggest struggles in quant !!! THANK YOU PHILIP

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Boss, You won't believe how much good work you are doing by making these videos. Seriously you will be the only one for my success in GRE. Deep Respect for you Philip. Salutes✌️ God Bless You !

[@TheTestedTutor]

Wow, thanks

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I love the English accent: "Give them names like A to Haytch" lol

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[@TheTestedTutor]

Glad you like them!

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My test (2nd trial) in 10 days, I first found your channel 1 day before my 1st trial. Your videos are so helpful and makes everything easy, thanks!

[@arundhatijoshi6303]

Please do the advance permutations and combinations questions.

[@marknelsonkumi9669]

Your explanations of the basic concepts under Combinations are lucid. Thanks so much, Philip. More power to your elbow.

[@peaceyusuf]

Taking the GRE In few weeks Thanks to your videos I am beginning to get little confidence 😊

[@jturlais]

I am so glad I found you to make math interesting before the GRE ;) You deserve the world!

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Thank you so much for this...the calmness with which you teach is just so admiring. I'll 100% recommend you to other aspirants as well. Thankyou for existing :)

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[@TheTestedTutor]

I'm so glad LC!

[@Dms100]

Thanks Philip! All your videos are extremely well done! Clear and concise.

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Thanks to your killer tip (2:52), I will never forget the combinations formula again. Thank you!

[@TheTestedTutor]

YAY! Go Lucy!

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[@TheTestedTutor]

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I take the test on the 27th and your videos have helped me get prepared. Thanks!

[@TheTestedTutor]

Best of luck Carol!

[@thee_swatirai]

I used to leave these questions out, as it seems to be really difficult.
But after watching your videos It seems I can do it and it's easy.
Thank you for making these videos.
Keep making! :>

[@jenniferzamudio4774]

Yes! Thank you for helping me remember these concepts, it's been a few years haha. It makes it more manageable 😊

[@TheTestedTutor]

Thank you so much Jennifer!

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I'm preparing for the GRE and your videos are really helpful! Thank you:)

[@TheTestedTutor]

Good luck!!

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Thanks for making these helpful videos ! Please keep posting more 😃

[@TheTestedTutor]

Thank you so much Pramita!

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[@TheTestedTutor]

So nice of you Varsha

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[@TheTestedTutor]

Yay!

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Taking my GRE tomorrow! Thanks for clearing this up for me!

[@TheTestedTutor]

Hope it went well Aubrie!

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I have been watching ur videos for quant
Thanks for all the efforts you kpt
One of the best channel ever found on yt 😊
Will recommend for all my frnds , sir ❤

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Absolutely amazing videos. Great explanations, and I love the examples!! Thank you so much

[@chimamakaanakwuo-nwosu6048]

I totally understand this topic now. Thank you so much Philip

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Yes Philip, it was FUN!

[@stanislavchladny6071]

Really great help for my upcoming GMAT exam. Looking forward to other useful videos. Great job you are doing there Phil!! :)

[@TheTestedTutor]

Thanks Stanislav!

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[@TheTestedTutor]

That's a compliment! Thanks neurobiogirl

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Just want to drop a comment and a thank you! all of your videos have been super helpful

[@TheTestedTutor]

Glad you like them!

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Thank you! Will eagerly wait for the advance permutations and combinations questions.

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Ok, there is clearly demand for it!

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God bless you and your heart Philip for your efforts 👍

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thanks for the tip on remembering the formula! amazing!

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Gratitude for these videos!

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This formula is super easy to follow and I have not seen in the books I've been reviewing. Thank you so much, I feel more confident but still I would you guys wish me luck to rock it this Friday! :) Cheers!

[@TheTestedTutor]

Good luck Diana!

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Excellent tuition. Thank you...

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If I don't appreciate you, then I'll the null human on the earth.
Really appreciate you Sir
And much more love from Pakistan.
Adding one thing that kindly also upload videos for verbal section too.
😊

[@robbitpat]

This video gives me hope. Thanks a lot❤

[@Spybuoy]

Just a small note, representing 8! in 8C2 as (8 * 7 * 6!) helps in calculating the number of combinations in a more effective manner.
Would like a video which integrates combinations into probability.

[@fuadfataliyev3714]

Thanks a lot, Philip! You helped me a lot, tomorrow I have the GRE, so, let's see what happens :)

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You are the best that has happened to me in a long time... thank you!

[@TheTestedTutor]

What a lovely comment! Thanks Michelle

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Thank you. This was really helpful

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You are awesome!! Making a scary subject easier to get going. Thanks!

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You are great at what you are doing.

[@pascalekeh]

Thanks for everything, Philip

[@desireegarza1802]

So much help, thank you!

[@hannahforsythe3847]

Do you think you can do a video on how to spot a combination question vs permutation question?

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Awesome video. Thanks alot for your effort.

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Very nice and simple explanation

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[@TheTestedTutor]

Glad it was helpful!

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You are honestly amazing

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Thank you :))

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Very good Mister Philip.

[@Damed001]

This was crazy helpful I’m glad I came across one of your comments in another video thank you! Is there a permutations video?

[@TheTestedTutor]

yep!

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Great work!

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Awesome, thanks!

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Watching all of your videos before tackling the practice questions in my Manhattan 5 lb. book!

[@TheTestedTutor]

You got this!

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Thank you Philip, this was helpful, going through all your videos from the begin.

[@TheTestedTutor]

Wow, keep going! Let me know feedback at the end.

[@adityabhat5189]

Thank you so much so making this video Phil! That last example was particularly helpful.
You are doing a fantastic job!
I'm looking forward to more of these type of quality videos.
Best Regards.

[@TheTestedTutor]

Thanks Aditya!

[@madhurimachaudhuri3282]

@@TheTestedTutor Het Philip, have you scored 340/340 in GRE in June 2019?( I mean did you score a 340 in GRE this year?)

[@TheTestedTutor]

@@madhurimachaudhuri3282 Yes, I have been a tutor for much longer but only recently decided to do the test for real. Got 340 first time.

[@madhurimachaudhuri3282]

@@TheTestedTutor I mean did you score 340 in GRE in June 2019?

[@TheTestedTutor]

@@madhurimachaudhuri3282 Yes, you can see the date on the score report. Why do you ask?

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Been doing these practice problems knowing this was in my brain somewhere, thank you for rustling it out xD

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I was looking for a way to revise and brush up my concepts and all these videos helped me in achieving my goal. Thank you for making these videos.Really appreciate it.

[@TheTestedTutor]

Happy to help!

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Thank you so much

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Thank you!

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You've helped Alot

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The best thing about you is that you can simplify quant questions easier than anyone. I had no idea about combination watching so many stuffs. But this time, it seems like I've learned something. I can't wait to be a part of your course.

[@TheTestedTutor]

Hope you like!

[@shafiabdullahhauque7933]

Thanks @@TheTestedTutor . I'm liking so far. But there are lots of materials to cover. I've subscribed for two courses. I'm still at 300 level. I don't know when I can finish them all.

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what a clever way to simplify smtg so mind boggling!!! Thank you!

[@TheTestedTutor]

So glad it was helpful Lela!

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Thanks ltgr!

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I am a lifesaver!

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THANKS!!! Permutations, please? I am presently studying for the GMAT.

[@TheTestedTutor]

Great idea Lilian!

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Thank you so much for this video :)

[@TheTestedTutor]

Thakns for the comment!

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Hey, can you do a video on more advanced questions? Thanks for this one!

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Amazing teacher 😀

[@TheTestedTutor]

Thank you! 😃

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I sit for my exam tomorrow and essentially decided that I was just going to get these problems wrong. Now I’m so excited to see one on my exam

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I'm glad!

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Lets give this man the appreciation

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Thank you!!!

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Thanks!

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I'm liking the vid because I am impressed he was able to do the problems

[@TheTestedTutor]

haha

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[@TheTestedTutor]

So glad Sweta!

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That was fun!

[@chandlerrock3342]

Thank you so much! Were you able to post a video on more advanced problems on this topic? I don't see it.

[@TheTestedTutor]

Not yet, hopefully soon!

[@chandlerrock3342]

@@TheTestedTutor Thanks for the reply, I'm looking forward to it! Your videos have completely brightened my studies this last week.