# Counting Principles

#### 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

#### slovakiamaths

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

#### ugkwan

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.

#### slovakiamaths

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

(Happy)

#### ugkwan

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

#### mr fantastic

MHF Hall of Fame
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).