If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is :

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Answer: D. {{945} \over {{2^{10}}}} Total ways of distribution = 410 = 220 Number of ways selecting two boxes out of four = 4C2 Then number of ways selecting 5 balls out of 10 = 10C5 Then no of ways of distributing 5 balls into two groups of 2 balls and 3 balls = 5C3.2! Then number of ways to distributing remaining balls into two boxes = 25 Number of ways placing exactly 2 and 3 balls in two of these boxes = 4C2 	imes 10C5 	imes 5C3.2! 	imes 25 = {{{{6.252.10.2.2}^5}} \over {{2^{20}}}} = {{945} \over {{2^{10}}}}

If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is :

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