JEE Main 202522 JanuaryMorning Shift
- Exam
- JEE Main
- Year
- 2025
- Date
- 22 January
- Shift
- Morning Shift
- Subject
- Mathematics
- Chapter
- Permutation and Combination
JEE Main 2025 · 22 January · Morning Shift · Mathematics · Permutation and Combination
From all the English alphabets, five letters are chosen and are...
From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is ' M ', is :
Options
- A
- B
- C
- D
Correct answer
A.
Step-by-step solution
\begin{aligned}
& \underbrace{A B}_{12} \quad \underbrace{\text{ MN........Z }_{13} \\
& =\underset{\substack{\text{ Selection of two } \\
\text{ leters before } \mathrm{M}}}{{ }^{12} \mathrm{C}_2} \times \underset{\substack{\text{ Selection of two } \\
\text{ leter after } \mathrm{M}}}{{ }^{13} \mathrm{C}_2}=5148
\end{aligned}