There are four balls of different colours and four boxes of colours same as those of the balls. The number of ways in which the balls, one each in a box could be placed such that a ball does not go to a box of its own colour is
A
7
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B
8
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C
9
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D
20
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Solution
The correct option is C9 We know that, if n different things are arranged in a row, then the number of ways in which they can rearranged, so that none of them occupies its original place is
n!(1−11!+12!−13!+...+(−1)nn!). Now, assume that each ball is placed in the box of its own color and apply the above result. Hence, the required number of different ways is. 4!(1−11!+12!−13!+14!)=4!2!−4!3!+1 =12−4+1=9