Question

How many four-letter distinct initials can be formed using the alphabets of English language such that the last of the four words is always a consonant? Select one:
a. 26³*21
b. 26*25*24*21
c. 25*24*23*21
d. 25*24*23*22

Answer 1

Answer:

The correct option is a. 26³*21

Explanation:

The question states that the last of the four letters must be a consonant and we have a total of 21 consonants (26 - 5) out of the 26 letters in the alphabets. So, we have a possibility of 21 letters that can be placed at the fourth position.  

The remaining three positions of the 4-letter initial can be a combination of all the 26 alphabets which means we have a possibility of 26 letters for each of the first 3 positions.

The number of distinct 4-letter initials that can be formed are:

26 x 26 x 26 x 21

= 26³ x 21  

Note: The question doesn’t specify that the letters used in the combination must be distinct hence we have considered all 26 alphabets to be placed at the first three positions.