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 :

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