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19 October, 01:39

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

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Answers (1)
  1. 19 October, 04:56
    0
    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.
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