WBJEE · Maths · Permutation Combination
A is a set containing n elements. \(P\) and \(Q\) are two subsets of \(A\). Then the number of ways of choosing \(P\) and \(Q\) so that \(P \cap Q=\varphi\) is
- A \(2^{2 n \space 2 n} C_n\)
- B \(2^n\)
- C \(3^n-1\)
- D 3^n
Answer & Solution
Correct Answer
(D) 3^n
Step-by-step Solution
Detailed explanation
\(\sum_{r=0}^n{ }^n C_r \cdot 2^{n-r}=(2+1)^n=3^n\) (Assuming \(P\) contains r elements then \(Q\) can be formed with \(n-r\) elements in \(2^{n-r}\) ways)
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