Question

In how many ways Can the letters of the word assassination be arranged so that all the S's are together?

Answer 1

Answer:

The word ASSASSINATION has three A's, four S's, two I's, two N's and T, O occurs only once.

We have to consider the case when all the S's together and so taking it as one packet or unit. So now we have three A's, one unit of four S's, two I's, two N's, one T, one O and thus a total of 10 units.

Therefore the number of arrangements possible when all the S's is together

                         

Hence, the distinct permutations of the letters of the word ASSASSINATION when four S's  come together = 151200

Answer 2

$\mathsf{\huge{\fbox{ \: \: SOLUTION \: \: }}}$

There are total 13 letters of which A occur three times , S occur four times , I occur two times , N occur two times

Assume the 4's together as a one letter

So, now , the total number of letters is a 10

Therefore , The number of permutations when all 4's occurs together is

$\sf = \frac{10!}{3! \times 2! \times !} \\ \\ \sf = \frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4!}{3 \times 2 \times 2 \times 2 \times 1} \\ \\ \sf = \frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4!}{4!} \\ \\ \sf = 151200$

Hence , 151200 is the number of permutations when all 4's occurs together