probability

[luvbug]

Problem: In a club with 8 male and 11 female members, how many 5-member committees can be chosen that have at least 4 women?

I found the probability of it with five women and with four women and added the numbers together. My answer: 118,800 ways.

 

[galactus]

I think that is a little too high.

There are only 5 chosen for the committee.

case 1, 4 women and 1 man:

\(\displaystyle \binom{11}{4}\cdot\binom{8}{1}\)

case 2, 5 women:

\(\displaystyle \binom{11}{5}\cdot \binom{8}{0}\)

add them up.

 

[luvbug]

Still a little confused. Are those fractions that you are having me multiply or are they permutations or a combination? Thanks

 

[Deleted member 4993]

Still a little confused. Are those fractions that you are having me multiply or are they permutations or a combination? Thanks

Those are standard notations for combinations.

 

[luvbug]

Okay. Thanks so much for your help.