In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?

Question

Philoid · Accepted Answer

In the given word ASSASSINATION, there are 4 ‘S’. Since all the 4 ‘S’ have to be arranged together so let as take them as one unit.

The remaining letters are= 3 ‘A’, 2 ‘I’, 2 ‘N’, T

The number of letters to be arranged are 9 (including 4 ‘S’)

Using the formula where n is number of terms and p₁, p₂ p₃ are the number of times the repeating letters repeat themselves.

Here p₁= 3, p₂= 2, p₃ = 2

Putting the values in formula we get