Total number of ways placing 10 different balls in 4 distinct boxes
=410 Since, two of the 4 distinct boxes contains exactly 2 and 3 balls.
Then, there are three cases to place exactly 2 and 3 balls in 2 of the 4 boxes.
Case-1: When boxes contains balls in order 2,3,0,5
Then, number of ways of placing the balls
=×4! Case-2: When boxes contains ball in order 2, 3, 1, 4.
Then, number of ways of placing the balls
=×4! Case-3: When boxes contains ball in order 2, 3, 2, 3
Then, number of ways of placing the balls
=×4! Therefore, number of ways of placing the balls that contains exactly 2 and 3 balls.
=×4!+ ×4!+ ×4! =25×17×945 Hence, the required probability
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