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In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S?

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

          (i) words start with P and end with S?

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There are 2 T's in word PERMUTATIONS, all other letters appear at once only.

If words start with P and ending with S i.e. P and S are fixed, then 10 letters are left.

The required number of arrangements are 

                                                                    =\frac{10!}{2!}=1814400

 

 

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