# How do you calculate permutations of numbers?

Oct 31, 2014

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

Let $P \left(n , r\right)$ denote the number of permutations of $n$ items chosen $r$ items at a time. $P \left(n , r\right)$ 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

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

Hence, there are 720 possible 3-digit codes.

I hope that this was helpful.