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 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
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 11C3*10!/(2!*2!*2!).