permutation

[itishjain]

how many arrangements can be possible in word PERMUTATIONS if there is always 4 letters between P & S ........?????

[anon_econ]

Case 1: There is no T between P & S
8C4*4!*2!*(7!/2!)
Case 2: There is 1 T between P & S
8C3*4!*2!*7!
Case 3: Both Ts are between P & S
8C2*(4!/2!)*2!*7!

Add all three.

The explanation for the first case is: Select the 4 letters that r to be b/w P & S from among E,R,M,U,A,I,O and N, change their positions, allow the positions of P & S to be switched, treat the resulting block of 6 letters to be one object & arrange it along with the 6 remaining letters (since there are 2 Ts, u need to divide by 2!).