00:01
We are given that there are five boys and three girls.
00:04
In part a, we want to find the number of ways the children can be seated in a row of eight seats.
00:09
If the ends are to be occupied by boys.
00:13
So now, if i were to draw the eight seats, the first seat is by a boy and the last seat is by another boy.
00:24
So in between, there will be six kids.
00:29
So for the first boy, there is five choose one way since there are five boys.
00:35
And for the last boy, there's only left with four boys to choose one of them.
00:42
Now, these two boys are considered fixed, but between them, there is two factorial way of arranging, just this boy and this boy.
00:52
Now, in between, there are six children left here, so there is actually six factorial way of arranging the six kids within the six seats here.
01:04
So the number of ways the children can be seated in a row if both ends are to be occupied by boys would be 5 choose 1 times 4 choose 1 times 2 factorial times 6 factorial and so this is 2 88080 ways...