Question

four couples 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

Answer 1

C(n,r)=n!r!(n−r)!C(n,r)=n!r!(n−r)!The number of committees of 4 gentlemen =4C44C4⇒1⇒1The number of committees of 3 gentlemen,1 wife =4C3×1C14C3×1C1(After selecting 3 gentlemen only 1 wife is left who can be included)The number of committees of 2 gentlemen 2 wives =4C2×2C24C2×2C2The number of committees of 1 gentlemen 3 wives =4C1×3C34C1×3C3The number of committees of 4 wives =1∴∴ The required number of committees =1+4+6+4+1⇒16

Answer 2

Answer:16

Step-by-step explanation:

we have to select one person from each couple. so 2c1×2c1×2c1×2c1=16.☺