Question

How do you calculate permutations of numbers?

Answer 1

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)!}`.

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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.

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I hope that this was helpful.