The total number of ways to put four identical oranges and six distinct apples intofive distinct boxes is (
5+4−1
C4) . 56 = 70 × 56 To satisfy the criteria that each box contains two objects we make three cases(based onnumber of oranges to go into a box) 1. Two oranges in each of the two boxes and no oranges in the other three boxes. Number of ways =
5
C2 ×
6!
2!2!2!
= 900 2. Two oranges in one box, one orange in each of the two other boxes (5) × (
4
C2) ×
6!
2!2!1!1!
= 5 . 6 . 180 = 5400 3. One orange in each of the four boxes = 5
6!
2!1!1!1!
= 5 × 360 = 1800 The total number of ways = 900 + 5400 + 1800 = 8100 Probability =