If 10 different balls are to be placed in 4 distinct boxes at random, then the probability…

Question

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 :

Accepted Answer

Total ways of distribution = 410 = 220

Number of ways selecting two boxes out of four = 4C2

Then number of ways selecting 5 balls out of 10 = 10C5

Then no of ways of distributing 5 balls into two groups of 2 balls and 3 balls = 5C3.2!

Then number of ways to distributing remaining balls into two boxes = 25

Number of ways placing exactly 2 and 3 balls in two of these boxes

= 4C2 $$ \times $$ 10C5 $$ \times $$ 5C3.2! $$ \times $$ 25

= $${{{{6.252.10.2.2}^5}} \over {{2^{20}}}}$$

= $${{945} \over {{2^{10}}}}$$

Solutions · 1