Question

Find the number of permutations in the word “embarrass”.

Answer 1

=9!/2! 2! 2!
=9.8.7.6.5.4.3.2.1/2.2.2
=45360

Answer 2

504.

Explanation:

We are asked to find the number of permutations in the word “embarrass”.

We can see that embarrass has three repeating words that are a, r, s.

The number of permutations of n objects taken r at a time is
`n(c,r)=(n!)/((n-r)!)`.

`n(9,3)=(9!)/((9-3)!)`

`n(9,3)=(9!)/(6!)`

`n(9,3)=(9\cdot 8\cdot 7\cdot 6!)/(6!)`

`n(9,3)=(9\cdot 8\cdot 7)/(1)`

`n(9,3)=504`

Therefore, the number of permutations in the word "embarrass" is 504.