This problem is solved using gap method. As here no '
S ' is adjacent to each other so we have to put them in the gap. So first write all the letters other than '
S ' such a way that there is a gap between two letters.
Given word is MISSISSIPPI.
Here,
mathrm‌I=4 times,
mathrm‌S=4 times,
mathrm‌P=2 times,
mathrm‌M=1 time
_M_I_I_I_I_P_P_Those seven letters M, I, I, I, I, P, P can be arranged in
frac‌7!‌4!2! waysThose seven letters creates 8 gaps and we have to choose 4 gaps from those 8 gaps to put those four '
S ' letters.This can be done
‌8C4 ways.After placing those four '
S ' letters we can arrange them in
frac‌4!‌4! ways.Therefore, required number of words
=‌×‌8C4×‌=‌×‌8C4=7⋅‌6C4⋅‌8C4
