Problem – Gaps in Permutation (ISI Entrance)


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.

  • 0
  • 20
  • 120
  • 2400

Key Concepts


Permutations

Combinatorics

Number Theory

Check the Answer


But try the problem first…

Answer: 2400

Source
Suggested Reading

ISI Entrance, TOMATO Objective, Problem 145

Combinatorics by Brualdi.

Try with Hints


First hint

Arranging PESSIMISTIC generally in

$\frac{11!}{3!3!}$ ways

Second Hint

The letters P E M T C can be arranged in 5!=120 ways

Final Step

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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