JEE Main Math Class 12 Probability Part 1 Questions

Total number of ways placing 10 different balls in 4 distinct boxes =410
Since, two of the 4 distinct boxes contains exactly 2 and 3 balls.
Then, there are three cases to place exactly 2 and 3 balls in 2 of the 4 boxes.
Case-1: When boxes contains balls in order 2,3,0,5
Then, number of ways of placing the balls =

10!

2!×3!×0!×5!

×4!
Case-2: When boxes contains ball in order 2, 3, 1, 4.
Then, number of ways of placing the balls =

10!

2!×3!×1!×4!

×4!
Case-3: When boxes contains ball in order 2, 3, 2, 3
Then, number of ways of placing the balls =

10!

(2!)2×(3!)2×2!×3!

×4!
Therefore, number of ways of placing the balls that contains exactly 2 and 3 balls. =

10!

2!×3!×0!×5!

×4!+

10!

2!×3!×1!×4!

×4!+

10!

(2!)2×(3!)2×2!×3!

×4!
=25×17×945
Hence, the required probability
=

25×17×945

410

=

17×945

215