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GMAT Problem Solving (PS) | Re: Permutations Question

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ParmarKarishma wrote:

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

My approach:

Lets consider P_ _ _ _ S be a single letter.

The total number of letters in PERMUTATIONS = 12

6 letters would be consumed in P_ _ _ _ S, so we have to arrange 7 letters. Hence 7!

Now for the two Ts 7!/2! and for arranging four letters between P and S. (7!/2!) 4!

Is this the right solution? I am not sure if additional multiplication should be done for selecting

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