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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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