00:01
In this problem, we are given a group of 15 men and 10 women, and we need to choose a panel with four distinct officers.
00:09
The question is, how many of those panels will contain at least two women? so in this problem, if we were choosing a committee, order would not matter.
00:18
But here we have specific offices, so order does matter.
00:22
We will still use the combinations formula, which is ncr equals n factorial over r factorial times n minus r factorial.
00:30
But we will also adjust for the fact that there are four distinct offices.
00:34
So we set up our solution by counting the number of panels with at least two women, meaning the number with two women and two men, plus the number with three women and one man, plus the number with four women and no man.
00:49
So applying ncr in each case, before we adjust, we have 10 women choose to times 15 men choose to, plus 10.
01:10
10 women choose 3 times 15 men choose 1 plus 10 women choose 4 times 15 men choose 0.
01:26
But now we need to adjust for the fact that there are four offices here...