A is a set containing n elements, A subset P (may be void also) is selected at random from set A and the set A is then reconstructed by replacing the elements of P. A subset Q (may be void also) of A is again chosen at random. The probability that

Options

A. `2^(n)`
B. `4^(n)`
C. `2n`
D. `3^(n)`

Answer

b

Explanation

The set A has n elemeats. So, it has `2^(n)` sunbsets.
Therefore, set P can be chosen in`""^(2^(n))C_(1)` ways. Similarly, set Q can
also be chosen in `""^(2^(n))C_(1)` ways .
`because ` Sets P and Q can be chosen in `""^(2^(n))C_(1)xx""^(2^(n))C_(1)=2^(n) xx2^(n) = 4^(n)`
ways.