Statement-1 : The sum of the series \( { }^{n} C_{0} \cdot{ }^{m} C_{r}+{ }^{n} C_{1} \cdot{ }^{m} C_{r-1}+{ }^{n} C_{2} \cdot{ }^{m} C_{r-2}+\ldots \ldots+{ }^{n} C_{r} \cdot C_{0} \) is equal to \( { }^{n+m} C_{r} \), where \( { }^{n} C_{r} \) s and \( { }^{m} C_{r} \) s denotes the combinatorial coefficients in the expansion of \( (1+x)^{n} \) and \( P \) \( (1+x)^{m} \) respectively.
W.
Statement-2 : Number of ways in which \( r \) children can be selected out of \( (n+m) \) children consisting of \( n \) boys and \( m \) girls if each selection may consist of any number of boys and girls is equal to \( { }^{n+m} C_{r} \).
(A) Statement-1 is true, statement-2 is true ; statement-2 is a correct explanation for statement-1.
(B) Statement-1 is true, statement-2 is true ; statement- 2 is NOT a correct explanation for statement-1.
(C) Statement-1 is true, statement- 2 is false.
(D) Statement- 1 is false, statement- 2 is true.
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