How do you calculate permutations using the formula?

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How do you calculate permutations using the formula?

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Answer 1 · 2014-11-04T19:22:05

Permutations are the way to take n things from r possibilities. There is no uniqueness required of the arrangements either.

The formula is $\frac{n!}{(n - r)!}$ ${n!}/{(n - r)!}$ where n is the number of items and r is the number of arrangements.

The ! symbol is for factorials, which is denoted below:
$n! = n \cdot (n - 1) \cdot (n - 2) \cdot \dots \cdot 2 \cdot 1$ $n! = n * (n - 1) * (n - 2) * … * 2 * 1$

So let us say we wanted 5 permutations of 3. We have:

$\frac{5!}{(5 - 3)!}$ ${5!}/{(5 - 3)!$

Which simplifies to

$\frac{5!}{2!}$ ${5!}/{2!}$

Which is

$\frac{5 \cdot 4 \cdot 3 \cdot 2!}{2!}$ ${5 * 4 * 3 * 2!}/{2!}$

This becomes $5 \cdot 4 \cdot 3 = 60$ $5 * 4 * 3 = 60$

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How do you calculate permutations using the formula?

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