A) 10
B) 12
C) 16
D) None of these
Correct Answer: C
Solution :
[c] Case-I: The number of committees of 4 gentlemen \[{{=}^{4}}{{C}_{4}}=1\] Case-II: The number of committees of 4 wives \[{{=}^{4}}{{C}_{4}}=1\] Case-III The number of committees of 3 gentlemen and 1 wife \[{{=}^{4}}{{C}_{4-1}}{{\times }^{1}}{{C}_{1}}{{=}^{4}}{{C}_{3}}\times 1=4\] Case IV The number of committees of 2 gentlemen, 2 wives \[{{=}^{4}}{{C}_{2}}{{\times }^{2}}{{C}_{2}}=6\] Case V The number of committees of 1 gentlemen, 3 wives \[{{=}^{4}}{{C}_{4-3}}{{\times }^{3}}{{C}_{3}}{{=}^{4}}{{C}_{1}}{{\times }^{3}}{{C}_{3}}=4\] Total number of req. committees \[=Case\left( I+II+III+IV+V \right)\] \[=1+1+4+6+4=16\]
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