MCQ
$\sum_{\substack{i, j=0 \\ i \neq j}}^{n}{ }^{n} C_{i}{ }^{n} C_{j}$ is equal to
- ✓$2^{2 n }-{ }^{2 n } C _{ n }$
- B$2^{2 n -1}-^{2 n -1} C _{ n -1}$
- C$2^{2 n }-\frac{1}{2}{ }^{2 n } C _{ n }$
- D$2^{ n -1}+{ }^{2 n -1} C _{ n }$
$=\sum_{ i =0}^{ n }{ }^{ n } C _{ i } \cdot \sum_{ j =0}^{ n }{ }^{ n } C _{ j }-\sum_{ i = j =0}^{ n }\left({ }^{ n } C _{ i }\right)^{2}$
$=\left(2^{ n }\right)\left(2^{ n }\right)-{ }^{2 n } C _{ n }$
$=2^{2 n }-{ }^{2 n } C _{ n }$
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