JEE Advance - Mathematics (1990 - No. 5)
A is a set containing $$n$$ elements. $$A$$ subset $$P$$ of $$A$$ is chosen at random. The set $$A$$ is reconstructed by replacing the elements of $$P.$$ $$A$$ subset $$Q$$ of $$A$$ is again chosen at random. Find the probability that $$P$$ and $$Q$$ have no common elements.
$$\left( \frac{1}{2} \right)^n$$
$$\left( \frac{2}{3} \right)^n$$
$$\left( \frac{3}{4} \right)^n$$
$$\left( \frac{1}{4} \right)^n$$
$$\left( \frac{5}{6} \right)^n$$
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