00:02
From a group of 12 boys and 10 girls, a committee of three students is chosen at random.
00:07
What is the probability that all three members on the committee will be girls? what is the probability that all three members on the committee will be boys? what is the probability that there will be at least one girl on the committee? let's take a look.
00:20
All girls.
00:21
We have a total of 22 people.
00:22
10 girls plus 12 boys gives us 22 total.
00:25
So i can pick from the 10 girls and we have three combinations out of that total of 22 people.
00:33
This gives us 10.
00:36
I start with 10 girls.
00:37
If i pick one girl, i have nine girls left, and then i have eight girls left.
00:41
We're going to stop there because we only have three people in this committee, divided by three people that i need for the committee, then i need two people for the committee, and then i need one more person for the committee.
00:52
And we do the same thing on the bottom, 22 times 21 times 20, divided by three times two times one.
00:59
That's going to cancel out because anything divided by itself is one.
01:03
So i have 10 times nine times eight over 22 times 21 times 20.
01:10
We can start reducing this.
01:12
10 goes into 22 times 10 divided by 10 is one.
01:16
20 divided by 10 is two.
01:18
This gives me nine times eight over 22 times 21 times two.
01:23
Eight goes into two or actually two goes into eight four times eight divided by two is four.
01:29
Two divided by two is one.
01:30
I have nine times four over 22 times.
01:33
21.
01:36
4 and 22, well, 4 divided by 2 is 2, 22 divided by 2 is 11.
01:43
So i get 9 times 2 over 11 times 21.
01:55
This gives me 18 over 11 times 21.
02:06
Actually, let's look at the 9 and the 21.
02:07
They're both divisible by 3.
02:09
9 divided by 3 is 3.
02:11
21 divided by 3 is 7.
02:13
So now we have 3 times 2 over 11 times 7.
02:17
Which gives me six over 77.
02:21
What about the odds of having all boys? we do something very similar, except now i have the 12 boys.
02:30
Instead of here i had 10 girls, we've got the 12 boys over the 22 total.
02:35
And then the same rules apply.
02:37
I've got 12 times 11 times 10 divided by three times two times one over 22 times 21 times 20 divided by three times two times two times.
02:50
Times one.
02:51
That's going to cancel out.
02:55
And i get 12 times 11 times 10 over 22 times 21 times 20.
03:01
Let's go ahead and start canceling.
03:03
10 divided by 10 is 1.
03:05
20 divided by 10 is 2...