00:01
Women and five men and need to get a committee of six.
00:03
So let's first of all figure out how many different committees we can have.
00:07
There's 15.
00:09
The order doesn't matter because we don't say the first person is president, et cetera.
00:14
So we're going to have a combination of 15 taking six at a time.
00:18
So i'm going to go to my calculator and get that value.
00:23
So i'm going to say 15 and then i'm going to go time and there's going to be 5 ,05 ways to pick that committee.
00:36
Now for the first one, it wants to know how many ways can we pick a committee with no women? well, it's going to be zero.
00:44
There's only five men.
00:46
So if we need six on a committee, we're going to have to have at least one woman.
00:50
So that probability is going to be zero.
00:52
What is the probability that it contains exactly two women? okay, so we want to know how can we pick the two women? how can we pick the two women.
01:01
Okay, so we need a combination of 10 picking two at a time because the order doesn't matter.
01:07
And then we want to know which two.
01:10
So how doesn't, so we're going to say a combination picking two at a time.
01:16
So let's go figure that out.
01:20
Ten, and we're going to pick two.
01:23
So that's going to be 45 different ways we can pick two women.
01:29
So now we're going to also know for the five men they're going to be the other four on the committee.
01:35
So we're going to have a combination of five, picking four at a time.
01:39
That's going to be five.
01:40
Now, again, we don't know which two are the women and which three, i mean, which four are the men.
01:47
So we're going to have to say we need a combination of six picking two at a time to know which ways the women can be put onto the committee.
01:56
So i'm going to go 06 and picking two at a time.
02:02
That's going to be 15.
02:04
We're going to multiply all those together...