How many different four letter words with the 1st letter M and the last letter S can be formed using the letters of the word "MATHEMATICS.

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.