Combinatorics monster???

Mayank is watching a monster TV show and Akul is studying mathematics. Suddenly a constructive interference occurs between the two. Mayank writes the word Mathematics 2015 times and asks Akul :-

How many words can be made with the letters of the word MATHEMATICS so that the M's and T's come alternatively and the letters appear exactly 2015 number of times as they appear in the word MATHEMATICS?

Akul, not so good in mathematics, decides to take help of his brilliant friends. Help him please...

The answer is in the form \( d\times(\frac{a!}{b!\times c!\times e!^{5}})\)

where a, b, c, d and e are integers and d is the minimum integer possible. Give your answer as a+b+c+d+e.

Details and Assumptions

  • By alternatively I mean that there is only one T between two cosecutive M's and vice versa.
  • Letters appear 2015 times means that if a particular letter appears n times in word MATHEMATICS, it will appear 2015n times in the word formed.

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