Counting Principles

Feb 2010
52
0
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
 
Apr 2010
41
15
India
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
 
Feb 2010
52
0
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.
 
Feb 2010
52
0
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

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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).