AIEEE 2008 Solved Paper

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
=‌

7!

4!2!

×‌8C4×‌

4!

4!

=‌

7⋅6!

4!4!

×‌8C4
=7⋅‌6C4⋅‌8C4