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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?


${26^3} × 21$


$26 × 25 × 24 × 21$


$25 × 24 × 23 × 21$


$\text{None of these}$

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Option(A) is correct

The last of the four letter words should be a consonant. Therefore, there are $21$ options.

The first three letters can be either consonants or vowels. So, each of them have $26$ options. Note that the question asks you to find out the number of distinct initials and not initials where the letters are distinct.

Hence answer,

$= 26×26×26×21$

$= 26^3 × 21$

(1) Comment(s)


Phrasing is confusing. By saying "4 letter distinct initials" it sounds like each letter cannot be repeated.

"Such that the last of the four words" should reach "Such that the last of the four letters"