# Combinations of"" problem

• Dec 24th 2012, 08:26 AM
lhurlbert
Combinations of"" problem
How many committed of size 15, from a group of 20 men and 30 women, contain both genders?

what I find difficult is the difference of numbers within the gender where if it were just 50 people taken 15 at a time id have no problem.

thanks :)
• Dec 24th 2012, 09:04 AM
Plato
Re: Combinations of"" problem
Quote:

Originally Posted by lhurlbert
How many committed of size 15, from a group of 20 men and 30 women, contain both genders?

There is a total of $\binom{50}{15}$ possible committees

Of those $\binom{20}{15}$ are all male and $\binom{30}{15}$ are all female.

Subtract those off. The committees left are mixed genders.
• Dec 24th 2012, 10:06 AM
lhurlbert
Re: Combinations of"" problem
And that's combination? I haven't seen that notation () yet
• Dec 24th 2012, 10:31 AM
Soroban
Re: Combinations of"" problem
Hello, lhurlbert!

Quote:

And that's combination?
I haven't seen that notation () yet.

Yes, that is an alternative symbol for combinations.

. . ${50\choose15} \;=\;_{50}C_{15} \;=\;\frac{50!}{15!\,35!}$