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 =

Question

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 =, 120, 14400, 21600, 86400

MARKS App · Accepted Answer

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 .

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