00:01
In this problem, it is said that a group of four women and six men must select a five -person committee.
00:07
We need to determine certain probabilities.
00:10
So, first of all, let us determine the total number of outcomes in this case.
00:19
So we have a total of four women and six men.
00:24
So that means there are four plus six people.
00:28
And out of them, we need to select any five people to form a committee.
00:32
So this can be done in 4 plus 6c5 ways.
00:36
Here we use c which represents combination.
00:39
And we use combination and not permutation in this case because the order of selection of the people does not matter.
00:46
So we end up with 4 plus 6, that's 10, 10c5.
00:50
So we have 10 factorial by 5 factorial times the factorial of 10 minus 5, that is 5.
00:58
And if we calculate this, this is equal to 252.
01:01
So, the total number of outcomes is 252.
01:05
Now let us determine the probabilities.
01:08
So in the first subpart, we have been asked to find the probability of getting a committee of three women and two men.
01:15
So the probability is the number of favorable outcomes divided by the total number of outcomes.
01:19
We determine the total number of outcomes to be 252, so i'm writing that in the denominator.
01:24
And now we have to find the number of favorable outcomes.
01:27
So the number of favorable outcomes will be the number of ways three women and two men can be selected.
01:34
So that means out of the four women, any three women need to be selected, and that can be done in four c3 ways, because the order of selection doesn't matter...