How do you calculate permutations of numbers?

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Answer 1 · 2014-10-31T07:51:38

Permutations are arrangements of items, so the number of permutations is the number of arrangements of items.

Let $P(n,r)$ denote the number of permutations of $n$ items chosen $r$ items at a time. $P(n,r)$ can be found by

$P(n,r)=n cdot (n-1) cdot (n-2)cdot cdots cdot(n-r+1)={n!}/{(n-r)!}$ .

Example

How many 3-digit codes are possible if each digit is chosen from 0 through 9, and no digits are repeated.

We can think of 3-digits codes as permutations of $10$ digits chosen $3$ digits at a time since no digits are repeated. So, we have

$P(10,3)=10 cdot 9 cdot 8=720$ .

Hence, there are 720 possible 3-digit codes.

I hope that this was helpful.