There are 5 students in a class, and there are 5 cricket bats and 5 footballs…

Concept: When two picks happen one after another without replacement, the probability that both picks satisfy a condition is the product of the first pick's probability and the second pick's conditional probability given the first pick already happened: P(both) = P(first) x P(second | first).

1. Total items available to pick from = 5 cricket bats + 5 footballs = 10 items.

2. Rohan picks first. Probability he picks a cricket bat = 5 bats out of 10 items = 5/10.

3. After Rohan removes one bat from the pool, 9 items remain, of which 4 are cricket bats.

4. Sunil picks next. Probability he also picks a cricket bat, given Rohan already picked one, = 4 bats out of 9 remaining items = 4/9.

5. Combined probability that both pick a cricket bat = (5/10) x (4/9) = 20/90 = 2/9.

Cross-check by direct counting: the two bats can be assigned to Rohan and Sunil in order in 5 x 4 = 20 ways, while any two of the 10 items can be assigned to them in order in 10 x 9 = 90 ways, giving the same 20/90 = 2/9.

So the probability that each of them picks up a cricket bat is 2/9.