Duration: 11:53

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\( A \) is a set containing \( \mathrm{n} \) 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
\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|}{ Column-I } & \multicolumn{2}{|c|}{ Column-II } \\
\hline A. & \( \begin{array}{l}\text { Number of elements in } P \text { is equal } \\
\text { to the number of elements in } Q \text { is }\end{array} \) & p. & \( \frac{{ }^{2 n} C_{n}}{4^{n}} \) \\
\hline B. & \( \begin{array}{l}\text { The number of elements in } P \text { is } \\
\text { more than that in } Q \text { is }\end{array} \) & q. & \( \frac{\left(2^{2 n}-{ }^{2 n} C_{n}\right)}{2^{2 n+1}} \) \\
\hline C. & \( P \cap Q=\phi \) is & r. & \( \frac{{ }^{2 n} C_{n+1}}{2^{n}} \) \\
\hline D. & \( Q \) is subset of \( P \) is & s. & \( \left(\frac{3}{4}\right)^{n} \) \\
\hline & & t. & \( \frac{{ }^{2 n} C_{n}}{4^{n-1}} \) \\
\hline
\end{tabular}
(a) \( \mathrm{A}-\mathrm{p}, \mathrm{B}-\mathrm{q}, \mathrm{C}-\mathrm{s}, \mathrm{D}-\mathrm{s} \)
(b) \( \mathrm{A}-\mathrm{r}, \mathrm{B}-\mathrm{p}, \mathrm{C}-\mathrm{s}, \mathrm{D}-\mathrm{q} \)
(c) \( \mathrm{A}-\mathrm{p}, \mathrm{B}-\mathrm{r}, \mathrm{C}-\mathrm{q}, \mathrm{D}-\mathrm{s} \)
(d) \( \mathrm{A}-\mathrm{r}, \mathrm{B}-\mathrm{s}, \mathrm{C}-\mathrm{p}, \mathrm{D}-\mathrm{q} \)
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