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There are four balls of different colors...

There are four balls of different colors and four boxes of colors same as those of the balls. Find the number of ways in which the balls, one in each box, could be placed in such a way that a ball does not go to box of its own color.

Text Solution

Verified by Experts

The correct Answer is:
9
The number of ways in which the ball does not go its own colour box `=4! (1 - (1)/(1!) + (1)/(2!) - (1)/(3!) + (1)/(4!))`
`=4! (1/2 - 1/6 + 1/24) = 24 ((12 - 4 + 1)/(24)) = 9`
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