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Q.

$\sum_{r = 0}^{6} (^{6} C_{r} \cdot^{6} C_{6 - r}) =$

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a

1124

b

1324

c

1024

d

924

answer is D.

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Detailed Solution

$\sum_{r = 0}^{6}^{6} {C_{r}}^{6} C_{6 - r} = \sum_{r = 0}^{6}^{6} C_{r}^{\cdot 6} C_{r} = \sum_{r = 0}^{6}^{6} C_{r}^{2} =^{12} C_{6} \Rightarrow \sum_{r = 0}^{6}^{6} {C_{r}}^{6} C_{6 - r} = \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7}{1 \times 2 \times 3 \times 4 \times 5 \times 6} = 924 .$

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