Question

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

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Solution

Finding the possible combinations:We know that, there are $26$ alphabets of English Language.Out of $26$, $5$ are vowels and $21$ are consonants. In the question, they have not mentioned that the letters cannot be repeated. Therefore,The first, the second, third and fourth letter can have any of the $26$ letters but the fifth letter should be a consonant.Thus the possibilities for fifth letter are $21$.Therefore, by multiplication principle, total number of possibilities are:$=26×26×26×26×21$$=9596496$.Hence, the total number of possible combinations is $9596496$.

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