Permutation and Combination  Quant/Math  CAT 2016
Question 4 the day:
September 04, 2003
The question for the day is from the topic Permutation and Combination.
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?
(1) (26^3)*(21)
(2) 26*25*24*21
(3) 25*24*23*21
(4) None of these.
Correct Answer  (1)
Solution:
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
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