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There are four balls of different colour...

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 in each box, could be placed such thast a ball does not go to a box of its own colour is: (A) `|__4-1` (B) 9 (C) `|__3+1` (D) none of these

Text Solution

Verified by Experts

Clearly this is a problem of derangement of 4 objects.
Required number of ways,
`D(4)=4!{(1)/(2!)-(1)/(3!)+(1)/(4!)}=12-4+1=9`
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