What is n choose k? || formula, examples, Pascal's triangles

N choose k, a nickname for binomial coefficient n,k, is one of the most important number in discrete mathematics. It is defined as the number of ways to choose k objects out of the collection of n objects. In this videos, we fully explain what n choose k is, formula of n choose k in term of fraction of factorials, 2 examples, and relationship to the famous Pascal's triangle.
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[@nchoosekmath]

Anyone else obsess with 'n choose k' as much as I do?

[@chinemelumj5349]

Thank you for this clear and concise explanation.

[@dhruva.3206]

A very nice explanation.

[@nchoosekmath]

Thank you!

[@bb1257]

Excellent thank you very much! Your examples are very helpful. It helped me to see the various ways i could use n choose k.

[@c7hu1hu]

why couldnt the same logic be applied in saying "we just have to find 4 ways to place b"? Man this is STILL confusing. Im sorry but for me it's always been true; this the one branch of maths i hate the most. And i sooo want to love it, like you do. gods.

[@mohamedmouh3949]

thank you that was helpful

[@VibingMath]

Finally know your channel name meaning, yay!

[@nchoosekmath]

Yay!!!

[@graceinsideofsound]

Awesome vid as always! One of my students just taught me the identity: (n choose 2) + ( (n + 1) choose 2) = n^2. Is there a cool bijective proof of this?

[@alkankondo89]

Excellent! Yes, combinatorics is my favorite field of math. Also, I always thought "n choose k" is a clever name for a math-themed RUclips channel -- very unique!

[@nchoosekmath]

Thank you!

[@stuartsaint4581]

This is an excellent explanation, I could feel the lightbulbs going off in my head every ten seconds.

[@nchoosekmath]

Thank you. I am so glad you find the video helpful to you!!

[@Impillion]

Excellent video sir, thanks 👍🏻

[@kingnehmna7810]

Instead of counting you could have did rows times columns haha. Good video nonetheless

[@bruhhhwhat2783]

Where you from

[@nchoosekmath]

Thailand bro!

[@ceroorec2153]

dude, this is great! I am a math student who felt shaky on this stuff and had to click your video after I saw your name matched the topic. Thanks for the vid, it was very helpful.

[@aphiwechiliza5534]

i feel like one can also use this n choose k to practise magic

[@ventreste]

Thank you, this was very helpful.

[@nchoosekmath]

Glad it was helpful!