00:01
Okay, so we're going to have a talk show that is going to have four women and three men as panelists.
00:07
A asks, in how many different ways, can the panelists be seated in a row of seven chairs? so this one, we're not caring about who is men and who is women.
00:16
So this is going to just be the permutation, right? permutation because order matters of 7p7, right? meaning we have seven people.
00:31
We're going to put all seven of them.
00:32
To a permutation.
00:34
So i'm putting this in my calculator, seven, permutation, seven, and i get 5 ,040 different ways.
00:43
Okay.
00:44
For b, it says in how many ways can the panelists be seated if the men and women are to be alternated.
00:50
So now we're going to have woman, man, woman, man, woman, man, woman, right? so we know that it has to be like that, but these four can still be switched around in any way, and these three can still be switched around in any way, right? so what we need to do is we need to take four, choose four, four p4 for the women, and multiply that by 3p3 for the men, because the three men can still be alternate or changed in any way, and so can the women.
01:27
So i'm going to do that for permutation four is 24...