First slide

Permutations

Question

The number of ways in which all the letters of the word “COCONUT” can be arranged such that at least one C comes at odd place, is

Moderate

A

240
B

360
C

720
D

1080

Solution

We have letters C, C,O, O, N, U, T
Required number of ways
= Total number of ways – Number of ways when no C comes at odd place (when C’s come at even places)
$= \frac{7!}{2! 2!} -^{3} C_{2} \times \frac{5!}{2!} = 1080$

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