00:01
All right, in your question, you're told a company has 10 male and six female employees and needs to nominate three men and three women to form a bowling team.
00:11
How many different teams can be formed? okay, so what we want to do is first try to figure out how many groups of three men we could get out of the 10 men that we have, and how many groups of three women we can get out of the six women we have.
00:27
Then once we know that we'll be able to multiply those two values to get your overall probability.
00:34
Let's just say, for example, for a minute, that there are only two groups of three men.
00:38
There's going to be way more than that.
00:40
And let's say for, you know, just understanding purposes, we had five groups of three women.
00:47
Well, each of these groups of men, there's two of them, could work with or go with these five groups of women.
00:54
That's why we're multiplying here because, you know, i have two groups here.
00:58
I'd have one of them could go with each of the five groups.
01:02
That would be five total teams.
01:03
Or the other one could go with each of the five groups.
01:06
So that would be a total of ten teams.
01:10
So i said that just to explain why we're multiplying them once we find them.
01:15
Now what we're going to use here is a combination.
01:18
Combination is what we want to use here because we don't really care about the order.
01:25
And combination doesn't care about order when we order these.
01:28
Because i don't want to count the three same people just because i could rearrange those three same people.
01:38
They're still the three same people.
01:39
So that's what a combination does.
01:42
For the men, this is going to be 10 c3, which will give me 10 factorial over 3 factorial times 10 minus 3 factorial.
01:59
Okay, for the women, it's going to be 6c3, which would be 6 factorial over 3 factorial times 6 minus 3 factorial...