Question

Find the number of permutations of the letters of the word MISSISSIPPI. In how many of these 

(a) the 4s’s are together 

(b) the 4s’s are not together 

(c) begin with MISS

Answer 1

Total letters = 11, I = 4, S = 4, P = 2. 

∴ The total number of permutations 7 

4s’s are together can be taken as 1 unit i.e.

M	I	SSSS	P	Total
1	4	1	2	8

∴ The number of permutations = 8!/(4! x 2!)

(b) 4s’s are not together = Total number of ways – 4s’s are together

= 11!/(4! x 4! x 2!) - 8!/(4! x 2!) (C)

Begin with MISS: The remaining 7 letters can be arranged in 7!/(3! x (2!)²)

(d) Begin with SIP: The remaining 8 letters (I = 3, S = 3) can be arranged in 8!/3!²