The number of ways in which four letters can be chosen from the letters of the word “MATHEMATICS” Is

There are eleven letters in total of which M, A and T occur twice and H,I,C,S,E occur only once. If four distinct letters are selected then number of ways is 8C4 . If two pairs of identical letters are selected, the number of ways is 8C4 . If two pairs of identical letters are selected, the number of ways is 3C2 and if one pair of identical letters and two distinct letters are selected, then the number of ways is 3C1× 7C2  So, required number = 8C4+ 3C2+ 3C1× 7C2