In how many rearrangements of the word SCINTILLATING will no two ‘I’ come together?
Let us consider the following arrangement without the three I’s.
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 11C3 ways.
Having placed the I’s, now let us find out all possible arrangements of the remaining letters. i.e., all possible arrangements of
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 11C3*10!/(2!*2!*2!).