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How many words can be formed with the letters of the word ‘CASTLE’ when ‘O’ and ‘A’ occupying end places.

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How many words can be formed with the letters of the word ‘CASTLE’ when ‘O’ and ‘A’ occupying end places.

(a) 217

(b) 48

(c) 75

(d) 186

The question was asked in an online interview.

The doubt is from Counting in division Counting of Discrete Mathematics

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The correct choice is (b) 48

Best explanation: When ‘O’ and ‘A’ are occupying end-places => A.S.T.L. (CE). We can see that (CE) are fixed, hence A, S, T, L can be arranged in  4! Ways and (C, E) can be arranged themselves is 2! ways. So, the number of words formed =  4! x  2! = 48 ways.

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