JEE Advanced Model Paper 9 with solutions for online practice

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 =

8100

170×56

=

162

21875