Permutations

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Permutations: Learn

A permutation is an arrangement in which order is important. The notation for permutations is P(n,r) which is the number of permutations of "n" things if only "r" are selected.

For example, if 5 students take a test, then we could rank them by who got the best grade. That would be a case where order matters.

Let's assume that Alice (A), Brooke (B), Carol (C), Dominick (D), and Edward (E) all took the test, and that we want to give awards to students who received best and second-best scores. Then the possibilities could be:
AB, AC, AD, AE, BA, BC, BD, BE,
CA, CB, CD, CE, DA, DB, DC, DE,
EA, EB, EC, ED
(20 total possibilities)

But that's a lot of writing out possibilities! We can use a formula that involves factorials instead:

P(n,r) =
n!
(n-r)!
= number of total possible permutations

In our example above, we have 5 students (n) and we are concerned about ranking 2 of them (r).

P(5,2) =
5!
(5-2)!
=
5*4*3*2*1
3*2*1
=
5*4*3*2*1
3*2*1
= 5*4 = 20 possibilities.

Notice how after writing out the factorial in the fraction, you can start to reduce the fraction by canceling most of the factors. This makes factorials the easy way to find how many possible permutations are available.

Permutation: Practice

Find the number of permutations.

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P(,) =

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