Statement-1 : The sum of the series \( { }^{\mathrm{n}} \mathrm{C}_{0} \cdot{ }^{\mathrm{m}} \mathrm{C}_{\mathrm{r}}+{ }^{\mathrm{n}} \mathrm{C}_{1} \cdot{ }^{\mathrm{m}} \mathrm{C}_{\mathrm{r}-1}+{ }^{\mathrm{n}} \mathrm{C}_{2} \cdot{ }^{\mathrm{m}} \mathrm{C}_{\mathrm{r}-2}+\ldots \ldots .+{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}} \cdot{ }^{\mathrm{m}} \mathrm{C}_{0} \) 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 \( \mathrm{P} \) \( (1+\mathrm{x})^{\mathrm{m}} \) respectively.
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Statement-2 : Number of ways in which \( \mathrm{r} \) children can be selected out of \( (\mathrm{n}+\mathrm{m}) \) children consisting of \( \mathrm{n} \) boys and \( m \) girls if each selection may consist of any number of boys and girls is equal to \( { }^{\mathrm{n+m}} C_{r} \).
(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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