The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal to :

Step-by-step solution

AA, MM, TT, H, I, C, S, E (1) All distinct ^8 C ₅ 56 (2) 2 same, 3 different ^3 C ₁ ^7 C ₃ 105 (3) 2 same I^ st kind, 2 same 2^ nd kind, 1 different ^3 C ₂ ^6 C ₁ 18 Total 179