# Counting Principles

• May 21st 2010, 04:37 PM
ugkwan
Counting Principles
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
• May 21st 2010, 05:45 PM
slovakiamaths
Quote:

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
• May 21st 2010, 05:50 PM
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.
• May 21st 2010, 06:01 PM
slovakiamaths
ok ans is $^4C_1*^6C_2+^4C_2=66$
• May 21st 2010, 06:04 PM
slovakiamaths
(Happy)
• May 21st 2010, 06:22 PM
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
• May 23rd 2010, 12:18 AM
mr fantastic
Quote:

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

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