Q40 / 90 · JEE Main 2024 (08 Apr Shift 2) · Mathematics

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 :

  • Correct answer
    A
    179
  • B
    177
  • C
    181
  • D
    175

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 $\rightarrow 179$

Hence, the correct answer is option: 'A'.

Relevant Questions