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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? - Mathematics

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

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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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NCERT Class 11 Mathematics Textbook
Chapter 7 Permutations and Combinations
Q 11.3 | Page 148
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