Permutations

Original notes by: Lauren F.
Typed up by: Katelyn C

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Permutations

A permutation is a way, especially one of several possible variations, in which a set or number of things can be ordered or arranged.

*NOTE, it is different from a combination in that order matters, unlike a combination. Given the names Charli, Rachael, and Patrick, it doesn’t matter that I order them like Patrick, Charli, and Rachael in a combination, because it’s still just the three people. But, in a permutation, their order does matter, so they MUST remain in the original order of Charli, Rachael, and Patrick.

EX: How many words can be formed by using all the letters of the word DRAUGHT so that (a) vowels always come together and (b) vowels are never together.

There are two vowels, we treat them as 1.
Solution: 6!*2! = 1,440 answer
Because:
6(5)(4)(3)(2)(1)= 720
X 2(1) = 2
720 X 2 = 1,440

(B) Total possibilities:
7(6)(5)(4)(3)(2)(1) = 5,040
Number of cases when vowels are not together=
5,040 – 1,440 = 3,600 answers

*For more practice, visit:
Permutations Better Explained