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:

Step-by-step solution

Total number of ways in which 10 balls can be placed in 4 boxes = 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 ⇒ 4 10 ⇒ 2 20 Exactly two box contain 2 , 3 balls ⇒ C 2 4 × 2 × C 2 10 × C 3 8 × 2 5 Probability = C 2 4 × 2 × C 2 10 × C 2 8 × 2 5 2 20 = 945 2 10