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 :

We have to select 5 alphabets and arrange them in alphabetical order such that the middle term is M. 

M is the 13th term in the English alphabets. 

It means that we have to select 2 alphabets out of 12, and place it on the left hand side of M and 2 alphabets out of the remaining 13, and place it on the right hand side of M. 

For the left hand side of M: 

Number of ways in which we select 2 alphabets out of 12 = $$12_{C_2}$$

Number of ways in which we arrange the selected alphabets in alphabetical order = 1 (only one case will be possible) 

Total number of ways in which we select 2 alphabets out of 12 and arrange it in alphabetical order = $$12_{C_2}\times1=12_{C_2}=66$$

For the right hand side of M: 

Number of ways in which we select 2 alphabets out of 13 = $$13_{C_2}$$

Number of ways in which we arrange the selected alphabets in alphabetical order = 1 (only one case will be possible)

Total number of ways in which we select 2 alphabets out of 13 and arrange it in alphabetical order = $$13_{C_2}\times1=13_{C_2}=78$$

Number of ways in which we can select M and place it in the middle of 5 alphabets = 1 

Total number of ways in which we select 5 alphabets and arrange it in alphabetical order such that M is the middle term = $$66\times78\times1=5148$$

Hence, we can select 5 alphabets out of 26 and arrange it in alphabetical order in such a way that the middle term is M in 5148 ways. 

$$\therefore\ $$ The required answer is A.