Question:
in how many ways can the letters of the word PERMUTATIONS be arranged if there are always 4 letters between P and S?
Answer:
Given, word is PERMUTATIONS
Here P and S are fixed, so 10 letters are left, out of which 2 are T
So, 10 letters out of which 2 are T can be arranged in 10!/2! = 1814400 ways
Now, letters P and S can be arranged so that there are 4 letters between them, which can be done in 2*7 = 14 ways
Hence, required number of ways = 1814400 * 14 = 25401600
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