First slide

Permutations

Question

The letters of the word $C O C H I N$ are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before $C O C H I N$ is

Moderate

A

360
B

192
C

96
D

48

Solution

Letters appearing in the word $C O C H I N$ are $C, C, H, I, N, O$
Words appearing before $C O C H I N$ are of the form $C X - - - -$
where X is one of the letters $C, H, I, N$ and the four remaining
places can be filled by the remaining four letters.
Thus, the number of words before $C O C H I N i s (4) (4!) = 96$

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