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There are 5 balls of different colours and 5 boxes of colours the same as those of the balls. The no of ways in which the balls , one in each box can be placed such that a ball does not go to a box of its won colour is ???

There are 5 balls of different colours and 5 boxes of colours the same as those of the balls. The no of ways in which the balls , one in each box can be placed such that a ball does not go to a box of its won colour is ???

Grade:

1 Answers

Aman Bansal
592 Points
8 years ago

Dear pinak,

 # of ways to arrange the 5 colored balls so that no ball corresponds with the box of the same color is:

120(1 - 1 + 1/2 - 1/6 + 1/24 - 1/120) = 120[ (60 - 20 + 5 -1)/120 ] = 120(44/120) = 44 different ways.

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