a How many ways are the to arrange the letters in the word M

a.) How many ways are the to arrange the letters in the word MATHEMATICS?

B.) How many diffreent arrangements of letters in MATHEMATICS are there such that the first m appears before the first a?

Solution

1) Mathematics

There are 11 letters with m repeated 2 times, a 2 times, t 2 times,

Hence no of different arrangements =

B) Let ma be one arrangment,Then we have ma as one unit, then other 9 letters with t repeated 2 times.

no of possible ways =  ways