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 :

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Correct answer: A. 179

AA, MM, TT, H, I, C, S, E (1) All distinct ^8 C_5 arrow 56 (2) 2 same, 3 different ^3 C_1 × ^7 C_3 arrow 105 (3) 2 same I^ st kind, 2 same 2^ nd kind, 1 different ^3 C_2 × ^6 C_1 arrow 18 Total arrow 179

The number of ways five alphabets can be chosen from the alphabets...

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