00:01
A class has 12 girls and 10 boys, and for part a of the question, we are asked in how many ways can a committee of five consisting of three girls and two boys be chosen? so for this question, this is a question about combinations rather than permutations because the order of the people selected does not matter.
00:24
We are not told about specific positions within the committee, so we're just interested in what combination of three girls and two boys we have.
00:33
So the number ways to make this committee is, well we want three girls out of 12, so there are 12 choose three ways to pick three of the girls, and for each of these combinations of three girls there are 10 choose two ways to pick the two boys, and this comes out to 9 ,900.
01:05
So there are 9 ,900 different committees that can be made that are comprised of three girls and two boys.
01:14
For b we're asked for the the probability that a committee of five chosen at random from the class consists of three girls and two boys.
01:31
So to calculate this, we use the theoretical approach to probability.
01:34
It's equal to the number of ways that the committee can consist of three girls and two boys.
01:42
We calculated that in part a, that's 9900.
01:47
Maybe i'll just write it out in full.
01:51
And then we divide it by the total number of ways or the total number of committees that can be made with five people from this class.
01:58
Class.
02:01
So there's a total of 22 in the class...