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In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?

Q.11.    In how many ways can the letters of the word PERMUTATIONS be arranged if the

            (iii) there are always 4 letters between P and S?
 

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The letters of the word PERMUTATIONS be arranged in such a way that there are always 4 letters between P and S.

Therefore, in a way P and S are fixed. The remaining 10 letters in which 2 T's are present can be arranged in

                                                                                                                                                                                    =\frac{10!}{2!}  ways.

Also, P and S can be placed such that there are 4 letters between them in 2\times 7=14 ways.

Therefore, using the multiplication principle required arrangements 

                                                                                                   =\frac{10!}{2!}14=25401600

 

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