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We are given the word MATHEMATICS. The 4 letter words that we have to create have to start with M and end with S.
Now, for the letters at the 2nd and the 3rd place, we have 2 As, 2 Ts, H, E, M I and C to choose from.
We can choose the same letter for both the places or different letters. If we make them the same, we have two choices A or T.
If they are different, the 2nd can have 7 choices and the 3rd can have 6 choices. So we have a total of 6*7 = 42 ways. This with the 2 ways that we found earlier gives a total 44 ways.
Therefore we can form 44 four letter words using the letters of the word MATHEMATICS with the first letter as M and the second as S.
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