If the number of all possible permutations of the letters of the word M A T H E M A T I C S in which the repeated letters are not together is 90 X , then X =

Step-by-step solution

Given word M A T H E M A T I C S In above word Arranging other than repeated letters H , E , I , C , S is 5 × 4 × 3 × 2 × 1   = 120 In between there will be 6 gaps in that we need to fill this repeated letters i.e., = 6 ! 2 × 2 × 2 = 90 . So total possible arrangements is = 120 × 90   =   10800 .