Probability & Statistics (38 of 62) Permutations and Combinations - Example 3
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- Опубликовано: 29 сен 2024
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In this video I will find the permutation and combination of 5 colors in 5,4,3,2,1 spaces.
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Don't look at the formula, look at the process of solving problem, the importance is on the thought not the formula!
Permutation is just combination with order, consider taking 5 units from 5 units, for combination you only have 1 choice, while for permutation those 5 units can be re-arranged with different orders, so multiply with 5!, easy as it.
Same in other cases, multiply the result of combination with n! , you get permutation! (Be careful about what n is though, it may change.)
why nPn equals nP(n-1) ??(5P5 ,5P4)
i know i can derive this from the permutation equation ,because 0! and 1! are equal to 1 ,so i get the same result ,but still it's not something intuitive and i'm confused , could you please elaborate it !
Why not use the permutations formula similar in form to the combinations formula. The nPk=n!/(n-k)!
This is what we are using in our PreCalculus class
Allan 112358 Allan 112358 Yea I’m not even sure the meaning of what I asked back then.
What I think of merely of now is
n!/(n-k)! as the permutation formula for n objects distributed over k positions. the denom just truncating the multiplication in the numerator for k positions.
however if the order of the elements didn’t matter, we know that for k positions, k elements would over a set of k positions would be able to be distributed in k! ways. k(k-1)(k-2) etc.. till 1
Meaning that in theory the combinations*k!=permutations,
therefore combinations=permutations/k!,
so you have intuitive somewhat heuristic determination of
n!/(n-k)!, n!/(n-k)!k!
I teach PreCalcululus and Calc to kids now. That’s what I use in PreCalc and stats.
Should we look at it as if combinations are the number of columns
and permutations are a number of records for each column? Thanks
professor,
for permutations you can use the same formula that you use for combinations, but without a k! in the denominator
You made a mistake on the 5 combination and 2 spaces. The answer is 20, not 10.