Latest CAT Aptitude Question SOLUTION: A company decides a new identity code for all its employees. The identity code would comprise of five letter initials that can be formed using the alphabets of English language suc

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A company decides a new identity code for all its employees. The identity code would comprise of five letter initials that can be formed using the alphabets of English language such that the fifth letter is always a constant. How many such combinations are possible?
26^3 * 21^2
21^4 * 26
21^3 * 26^2
26^4 * 21

Asked In CAT Puneet (10 years ago)

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amrita  (10 years ago)

i guess its d cause
4 letters are choosen from 26 letters of english alphabets...4 positions can be filled up with 26 letters thus 26^4 and last last position can be filled up with only one of 21 letters(26-5) thus ans is d

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pavan  (4 years ago)

In the English alphabet there are 26 letters. Out of these 5 are vowels and the rest of them (21) are consonants.

No where in the question has it been mentioned the letters cannot be repeated. Thus, the first place can have any of the 26 letters. Like wise the second, third and fourth places can have any of the 26 letters too. The only restriction we have is on the last (fifth) letter which has to be a consonant and therefore, it can have only 21 possibilities

therefore ... 26^4*(26-5) is the possibility

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