Find in how many ways can letters of the word PESSIMISTIC be arranged such that no two S and no two I can come together along with S and I cannot come together.
Permutations
Combinatorics
Number Theory
Answer: 2400
ISI Entrance, TOMATO Objective, Problem 145
Combinatorics by Brualdi.
Arranging PESSIMISTIC generally in
$\frac{11!}{3!3!}$ ways
The letters P E M T C can be arranged in 5!=120 ways
Remaining 6 slots with six letters 3 S and 3 I can be arranged in $\frac{6!}{3!3!}$=20 ways. Then number of ways =2400
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