How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent ?

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Answer 1 · 2018-07-04T11:37:45

#38949120# words can be formed , in which no two "S"
are adjacent.

Number of letters in the word "MISSISSIPPI" is #11# of which

number of "S" are #4#. Let us consider the number of ways ,

where all four "SSSS" always occur together. We assume

"SSSS" as a single letter , then the umber of letters in the word

"MISSISSIPPI" becomes #8#. Hence they can be arranged in

#8 !# ways . Four "SSSS" can be arranged among themselves

in #4!# ways. Total number of words can be formed in

#T_s = 8! *4! =40320*24=967680# ways taking all "S' together.

In #11# letters they can be arranged in #T=11! =39916800#

ways. Number of jumbled words in which no two "S"are adjacent

is # J= T - T_s= 39916800-967680= 38949120# [Ans]