A) \[252\]
B) \[672\]
C) \[420\]
D) \[250\]
Correct Answer: A
Solution :
The committee can be formed in following ways. \[(1)3\] gentlemen and \[3\] ladies, it can be selected in \[^{8}{{C}_{3}}{{\times }^{4}}{{C}_{3}}\] ways \[(2)2\] gentlemen and \[4\] ladies, it can be selected in \[^{8}{{C}_{2}}{{\times }^{4}}{{C}_{4}}\] ways. \[\therefore \]Total number of ways \[{{=}^{8}}{{C}_{3}}{{\times }^{4}}{{C}_{3}}{{+}^{8}}{{C}_{2}}{{\times }^{4}}{{C}_{4}}\] \[=56\times 4+28\times 1\] \[=224+28\] \[=252\]
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