Hi, Im having a hard time defining the problem into a working equation

Forming a Committee: Four people are to be selected at random from a group of four couples. In how many ways can this be done under the following conditions?

a. The group must have at least one couple

Thanks

Originally Posted by ugkwan

Forming a Committee: Four people are to be selected at random from a group of four couples. In how many ways can this be done under the following conditions?

a. The group must have at least one couple

Thanks

Ans is : 4*6*5=120

It is not 120 b/c if I were to chose a combination of 4 people without regard to if they are a couple or not I would get 70.

nCr = 8C4 = 70

It is less than this I think.

ok ans is $\displaystyle ^4C_1*^6C_2+^4C_2=66$

Please explain your reason b/c the book says the answer is 54, I dont know how it got to 54.

How u figure it's 66? An explanation of how you broke down the word problem would help greatly. Thanks

Originally Posted by ugkwan

Hi, Im having a hard time defining the problem into a working equation

Forming a Committee: Four people are to be selected at random from a group of four couples. In how many ways can this be done under the following conditions?

a. The group must have at least one couple

Thanks

$\displaystyle {8 \choose 4} -$ (no. of ways choosing the group with no couples).