In how many ways can the letters of the word \"PERMUTATIONS\" be arranged so that there is always exactly 4 letters between P and S ?

          25401600                                                                                                         

9p4/2 because of two t in permutation so answer is 1512.

No.of letters=12 with T=2 times

no of words=10!/2!

now no. of ways.. in which- P[4letters]s=7[i.eP at1 and s at 6,p at2 sat 7..up to p at 7]

||ly  for =S[4 letter]P=7 ways

=>14 ways 

now,

no of ways=14*10!/2!=25401600

_ _ _ _ _ _ _ _ _ _ _ _ there are 12 letters and will be seven ways of fixing p and s i.e.,7C1 such that there are 4 letters in between them and two ways of interchanging p and s i.e.,2C1   and left with 10 letters in 10 spaces and T is repeated twice so    10!/2!         .........   so answer is (7c1*2c1**10!)/2!