JEE Main 2020 — Probability Question with Solution

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

= $$\frac{{\mathrm{6.252.10.2.2}}^5}{2^{20}}$$

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