JEE Main · 2020 · 09 Jan 2020 · Shift 2 · Permutations and Combinations

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:

Answer: (B)

Solution

Each of the

10

distinct balls can land in any of the

4

boxes, so there are

4^{10}

equally likely outcomes. For one box to hold exactly

2

balls and another exactly

3

, first choose which box takes

2

and which takes

3

4 \times 3 = 12

ways, then select the balls in

(2 10) (3 8)

ways, and let the remaining

5

balls fall into the other two boxes in

2^{5}

ways. The favourable count is

12 \cdot 45 \cdot 56 \cdot 32 = 967680

, and dividing by

4^{10} = 1048576

gives

\frac{945}{2 ^{10}}

JEE Main · 2020 · 09 Jan 2020 · Shift 2 · Single correct option