In how many ways can the letters of the word permutations be arranged if there are always 4 letters between p and s?

Here P and S are fixed, so 10 letters are left, out of which 2 are T's

So, 10 letters out of which 2 are T's 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

Required no. of ways = 1814400 * 14 = 25401600