# Permutation Formula

When objects or symbols are arranged in different ways and order, it is known as permutation.

Permutation can be done in two ways,

**Permutation with repetition:** This method is used when we are asked to make different choices each time and have different objects.

**Permutation without Repetition:** This method is used when we are asked to reduce 1 from the previous term for each time.

The formula for Permutation is as stated below:

\[\large Permutation=\:_{n}P_{r}=\frac{n!}{(n-1)!}\]

\[\large Permutation with Repetition=n^{r}\]

### Solved Examples

**Question 1: **Find the number of permutations if n = 9 and r = 2?

**Solution:**

Given n = 9 and r = 2

$Permutation=\:_{n}P_{r}=\frac{n!}{(n-1)!}$

$=\frac{9\times 8\times 7\times 6\times 5\times 4}{2}$ = 181440

**Question 2: **Find how many ways you can rearrange the word “BANANA” all at a time?

**Solution:**

Given words: BANANA

Total number of letters in “BANANA” = 6

Total number of “A” in the word “BANANA” = 3

Total number of “N” in the word “BANANA” = 2

so, the permutation = $\frac{6!}{3! 2!}$ = $\frac{6 \times 5 \times 4 \times 3!}{3! 2!}$ = 60