A) 12
B) 14
C) 16
D) 24
Correct Answer: C
Solution :
[c] The number of committees of 4 gentlemen \[{{=}^{4}}{{C}_{4}}=1\] The number of committees of 3 gentlemen, 1 wife \[{{=}^{4}}{{C}_{3}}{{\times }^{1}}{{C}_{1}}\] (\[\because \] After selecting 3 gentlemen only 1 wife is left who can be included) The number of committees of 2 gentlemen, 2 wives \[{{=}^{4}}{{C}_{2}}{{\times }^{2}}{{C}_{2}}\] The number of committees of 1 gentleman, 3 wives \[{{=}^{4}}{{C}_{1}}{{\times }^{3}}{{C}_{3}}\] The number of committees of 4 wives = 1 \[\therefore \] The required number of committees \[=1+4+6+4+1=16\]
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