Question

There are 5 different-colored boxes in a room each with a distinct cover. Find out the number of ways so that these covers can be put on the boxes such that none of the boxes can have right covers on it? (Assume that all the covers must be on the boxes).

(a) 208

(b) 137

(c) 239

(d) 24

The question was posed to me at a job interview.

I'd like to ask this question from Counting in portion Counting of Discrete Mathematics

Answer 1

The correct choice is (d) 24

To elaborate: Let the box covers be A, B, C, D and E. The possible ways for the covers to not be in the exact order of A, B, C, D, E are: 4! = 24 ways. (Since correct order i.e., A, B, C, D and E must be eliminated from such arrangements).