The value of \( { }^{n} C_{0} \times{ }^{2 n} C_{r}-{ }^{n} C_{1} \times{ }^{2 n-2} C_{r}+{ }^{n...
The value of \( { }^{n} C_{0} \times{ }^{2 n} C_{r}-{ }^{n} C_{1} \times{ }^{2 n-2} C_{r}+{ }^{n} C_{2} \times{ }^{2 n-4} C_{r}+\ldots \) is equal to
(1) \( { }^{n} C_{r-n} \times 2^{2 n-r} \) if \( r \geq n \)
(2) 0 , if \( rn \)
(3) \( { }^{n} C_{r-n} \times 2^{n-r} \) if \( r \geq n \)
(4) \( -{ }^{n} C_{r-n} \times 2^{2 n-r} \) if \( rn \)
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