JEE MAIN - Mathematics (2024 - 8th April Evening Shift - No. 16)
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:
179
177
175
181
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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