Four couples (husband and wife) decide to form a committee of four members. The number of different committees that can be formed in which no couple finds a place is

Options

A. 10
B. 12
C. 16
D. None of these

Answer

C

Explanation

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)xx""^(1)C_(1)=""^(4)C_(3)xx1=4`
Case IV : The number of committees of 2 gentlemen, 2 wives = `""^(4)C_(2)xx""^(2)C_(2)=6` ltBrgt Case V : The number of committees of 1 gentlemen, 3 wives = `""^(4)C_(4-3)xx""^(3)C_(3)=""^(4)C_(1)xx""^(3)C_(3)=4`
Total number of req. committees
=Case (I+II+III+IV+V)
=1+1+4+6+4=16