Verified Solution • 2025–26 Session moderate

QJEEM24Ma24aa: JEE Main 2024 Mathematics - Class 11 JEEM24Ma24aa Solution: The number of ways five alphabets can be chosen from the…

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:

Multiple Choice Options

A 179
B 177
C 175
D 181

Step-by-Step Verified Solution

$\begin{aligned} 2 M \\ 2 A \\ 2 T \\ H, E, I, C, S \end{aligned}$

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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