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

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

Option: 1

8640


Option: 2

4800


Option: 3

2400

 


Option: 4

5480


Answers (1)

best_answer

Arrange the remaining letters in 5! ways

      |\mathrm{P}| \mathrm{E}|\mathrm{M}| \mathrm{T} \mid \mathrm{C}
In the 6 gaps, arrange the  3 \ \mathrm{Ss} and 3 \ \mathrm{Is} in
\frac{6 !}{3 ! 3 !} \text { ways }=20
The answer is 5 ! \times 20=2400

 

Posted by

Divya Prakash Singh

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