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The number of ways in which the letters ...

The number of ways in which the letters of the word PESSIMISTIC can be arranged so that no two S's are together, no of two I's are together and letters `S` and `I` are never together is

A

A. `8640`

B

B. `4800`

C

C. `2400`

D

D. `5480`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` Arrange the remaining letters in `5!` ways
`|P|E|M|T|C|`
In the `6` gaps, arrange the `3Ss` and `3 Is` in
`(6!)/(3!3!)"ways"=20`
The answer is ``5!xx20=2400`
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