In how many rearrangements of the word SCINTILLATING will no two ‘I’ come together?

**Explanation:**

Let us consider the following arrangement without the three I’s.

_S_C_N_T_L_L_A_T_N_G_

No two I’s would come together if the I’s are placed in the blanks. So, the question boils down to first finding out the number of ways in which three blanks can be chosen out of 11 blanks. This can be done in

^{11}C_{3}ways.Having placed the I’s, now let us find out all possible arrangements of the remaining letters. i.e., all possible arrangements of

SCNTLLATNG

The number of ways in which SCNTLLATNG can be arranged is 10!/(2!*2!*2!)

Therefore, the number of rearrangements of the word SCINTILLATING where no two I’s would come together is

^{11}C_{3}*10!/(2!*2!*2!).
Jatin Chhabriya says

Can you explain how the no. of ways in which SCNTLLATNG can be arranged came to 10!/(2!*2!*2!) ?