Mathematics · Permutations and Combinations

JEE Main 2024 — 8 April, Shift 2 — Question 5

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 :

Option A:
175
Option B:
181
Option C:
177
Option D:
179
Correct

Answer: D

Step-by-step solution

AA, MM, TT, H, I, C, S, E

(1) All distinct ${ }^{8} \mathrm{C}_{5} \rightarrow 56$

(2) 2 same, 3 different ${ }^{3} \mathrm{C}_{1} \times{ }^{7} \mathrm{C}_{3} \rightarrow 105$

(3) 2 same $I^{\text {st }}$ kind, 2 same $2^{\text {nd }}$ kind, 1 different ${ }^{3} \mathrm{C}_{2} \times{ }^{6} \mathrm{C}_{1} \rightarrow 18$

Total $\rightarrow 179$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 8 April, Shift 2
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Combinations