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# Gaps in Permutation | TOMATO Objective Problem 145

## 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

Permutations

Combinatorics

Number Theory

## Check the Answer

Answer: 2400

ISI Entrance, TOMATO Objective, Problem 145

Combinatorics by Brualdi.

## Try with Hints

Arranging PESSIMISTIC generally in

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 =20 ways. Then number of ways =2400

Watch the video

## 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

Permutations

Combinatorics

Number Theory

## Check the Answer

Answer: 2400

ISI Entrance, TOMATO Objective, Problem 145

Combinatorics by Brualdi.

## Try with Hints

Arranging PESSIMISTIC generally in

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 =20 ways. Then number of ways =2400

Watch the video

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