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There are five balls of different colours and five 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 exactly one ball goes to a box of its own colour, isA. 9B. 24C. 45D. 120 |
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Answer» Let `b_(1),b_(2),......b_(5)` be five balls and `B_(1),B_(2),......,B_(5)` be five boxes. Then, Requried number of ways `sum_(r=1)^(5)(r^(th)" ball is placed in "r^(th)" box")xx("Remaining balls are placed in wrong boxes")` `=sum_(r=1)^(5)1xx4!{-1(1)/(1!)+(1)/(2!)-(1)/(3!)+(1)/(4!)}` `=sum_(r=1)^(5)(12-4+1)=45`. |
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