From all the English alphabets,five letters a | vedclass

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(D) There are $26$ English alphabets. We need to choose $5$ letters and arrange them in alphabetical order such that the middle letter is $M$.Since th

Vedclass · Accepted Answer

$5148$

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(D) There are $26$ English alphabets. We need to choose $5$ letters and arrange them in alphabetical order such that the middle letter is $M$.Since the letters must be in alphabetical order,once we choose the $5$ letters,there is only $1$ way to arrange them.For the middle letter to be $M$,we must choose $2$ letters from the $12$ letters that come before $M$ (i.e.,$A$ to $L$) and $2$ letters from the $13$ letters that come after $M$ (i.e.,$N$ to $Z$).The number of ways to choose $2$ letters from $12$ is $^{12}C_2 = \frac{12 	imes 11}{2} = 66$.The number of ways to choose $2$ letters from $13$ is $^{13}C_2 = \frac{13 	imes 12}{2} = 78$.The total number of ways is $^{12}C_2 	imes ^{13}C_2 = 66 	imes 78 = 5148$.

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:

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