If a permutation of all 26 letters of the english alphabet is chosen at random, what is the probability that the permutation contain the letters MATHS in the same order (A doesn't come before M , T doesn't come before A , H doesn't come before T , S doesn't come before H). The probability can be expressed as where and are positive coprime integers. Find the value of .
Details and Assumptions
For example: "MATHSBCDEFGIJKLNOPQRUVWXYZ" is a valid sequence and so is "MPAQTRHSBCDEFGIJKLNOUVWXYZ", as order of letters of MATHS is maintained
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There will be the same number of permutations of all 2 6 letters for each of the 5 ! = 1 2 0 possible permutations of the letters M , A , T , H , S , so the probability that the letters M , A , T , H , S appear in that precise order (as described in the question) in a randomly chosen permutation of the 2 6 letters of the English alphabet is 1 2 0 1 . Thus m + n = 1 + 1 2 0 = 1 2 1 .