JEE MAIN - Mathematics (2020 - 9th January Evening Slot - No. 1)
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 :
$${{965} \over {{2^{11}}}}$$
$${{965} \over {{2^{10}}}}$$
$${{945} \over {{2^{11}}}}$$
$${{945} \over {{2^{10}}}}$$
Explanation
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
= $${{{{6.252.10.2.2}^5}} \over {{2^{20}}}}$$
= $${{945} \over {{2^{10}}}}$$
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
= $${{{{6.252.10.2.2}^5}} \over {{2^{20}}}}$$
= $${{945} \over {{2^{10}}}}$$
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