In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
The letters have to be arranged in such a way that there are always 4 letters between P and S.
Therefore, in a way, the places of P and S are fixed. The remaining 10 letters in which there are 2 Ts can be arranged in 10!/2! ways
Also, the letters P and S can be placed such that there are 4 letters between them in 2 × 7 = 14 ways.
Therefore, by multiplication principle, required number of arrangements in this case
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