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 :

Question

Aicharya · Accepted Answer

$\begin{aligned}
& \underbrace{A B}_{12} \quad \underbrace{\text { MN........Z }}_{13} \\ & =\underset{\substack{\text { Selection of two } \\ \text { leters before } \mathrm{M}}}{{ }^{12} \mathrm{C}_2} \times \underset{\substack{\text { Selection of two } \\ \text { leter after } \mathrm{M}}}{{ }^{13} \mathrm{C}_2}=5148
\end{aligned}$ ,

From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total…

Solution