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:
JEE · Math · previous-year question
- A.179correct
- B.177
- C.175
- D.181
Answer
A. 179
Explanation
$$\begin{aligned} & 2 M \\ & 2 A \\ & 2 T \\ & H, E, I, C, S \end{aligned}$$ Case-I 2 Alike 2 Alike 1 Diff $${ }^3 C_2 \times{ }^6 C_1=18$$ Case-II 2 Alike + 3 Diff $${ }^3 C_1 \times{ }^7 C_3=105$$ Case-III All different $${ }^8 C_5=56$$ Total ways $$=179$$
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