Maths is good for you

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 \(\frac mn\) where \(m\) and \(n\) are positive coprime integers. Find the value of \(m+n\).

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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