00:01
So for this problem, all of the calculations will be done using the binomial coefficient, or the choose function, where we have n choose r, is calculated as n factorial, divided by n minus r factorial times r factorial, where this is the number of ways to choose are things from a set of n.
00:25
So, first of all, i'll note that the total number of ways to arrange our, or group would be the number of ways to get a group of five out of a total set of 15.
00:38
So that's going to be 5 factorial divided by 16 minus 5.
00:43
So that's 11 factorial times 5 factorial.
00:48
So, one second here, something's gone wrong.
00:53
Oh, pardon me, that should be 11 factorial or 16 factorial at top.
00:56
Not okay, yeah.
00:58
So we'd have 4 ,368 total possible committees to form.
01:02
Out of our group of 16 people.
01:05
Now for part a, the probability of three women and two men would be equal to the number of ways to get three women out of the set of 10, so that's 10 choose three, times the number of ways to get two men from the set of six.
01:25
So times six choose two, and then we divide that by our grand total.
01:32
So 10 choose 3.
01:34
Now i'm going to note that, since i've gone through the calculation of that explicitly once, from this point on, i'm just going to be using the built -in functionality from my software here.
01:44
So like 10 choose 3 is going to be the same thing as doing 10 factorial over 7 factorial times 3 factorial.
01:52
So we'd have 10 choose 3 times binomial 6 choose 2, by to buy 4 ,000.
01:58
368 for a probability of about 0 .4 .121...