00:01
In this problem, we have been asked in how many ways can three boys and four girls sit in a row if the boys and girls must alternate.
00:09
So note that we will have one, two, three, four, five, six, seven spaces for these three boys and four girls to sit because there are a total of three plus four people.
00:25
Now, the boys and girls must alternate.
00:28
So, for example, if we start marking the boys from here, let's put a boy here.
00:35
We can't put a boy over here because the boys and girls must alternate.
00:40
So two boys can be next to each other.
00:42
So we must have a boy over here and the next boy can be over here.
00:47
But if we do that and we try to start setting the girls, then we can see that at the end over here, we end up with two girls who are sitting next to each other.
00:57
So this is not going to work.
00:59
On the other hand, if we suppose put this boy over here, then also we're going to end up with two girls sitting next to each other.
01:06
So that means we cannot have a boy in the first place.
01:11
That's not going to work.
01:12
So instead, what we will do is place a boy over here.
01:16
And since boys and girls must alternate, the second one goes here and the third one goes here...