Question

Determine the no. of permutations
for the word PHOTOGRAPH​

Answer 1

Given:

The word is "PHOTOGRAPH​".

To find:

The no. of permutations for the given words.

Solution:

The total number of letters in the word PHOTOGRAPH is 10.

It is clear that P, H, O are twice and T, G, R, A are occurred once.

To find the total number of permutations, we need to divide the permutation of 10 letters by the permutation of repeated letters.

The total number of permutations for the given word is

`Permutations=(10!)/(2!2!2!1!1!1!1!)`

`Permutations=(10* 9* 8* 7* 6* 5* 4* 3* 2* 1)/(2* 2* 2)`

`Permutations=10* 9* 7* 6* 5* 4* 3* 2* 1`

`Permutations=453600`

Therefore, the no. of permutations for the word PHOTOGRAPH is 453600.