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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