00:01
Four runners are taking a foot race.
00:03
We want to know how many ways there are for the race to finish when we know there could be times.
00:09
Okay, so for example, one way would be they are all first place.
00:14
They all finish at exactly the same time.
00:16
That's one option.
00:18
Maybe three finish in first, the next finishes in second.
00:25
Maybe we have two finish in first, two finish in second.
00:32
Maybe we have two finish in first, one finishes in second, one finishes in third.
00:44
Maybe we have one in first place, three in second place.
00:51
One in first place, two in second place, one in third.
00:57
Maybe we have one in first, one in second, two in third.
01:05
Third.
01:05
Or maybe we have one in first, one in second, one in third, and then one in fourth place.
01:14
So i've just listed out, just very systematically, all of the different combinations of ties we might get here.
01:23
Next, i want to know how many ways each of these could happen.
01:27
Let's start with all in first place.
01:29
There's only one way that could happen.
01:30
They all finish first.
01:32
What about three finish in first, one finishes in second? well there are four ways that could happen.
01:38
I'm thinking of four choose three or four choose one.
01:42
You have four runners, you are picking three to be first place or you're picking one to be second place.
01:48
So we're using combinations here.
01:51
Well really technically we're using permutations.
01:54
It's kind of a combination of the two.
01:56
I need to worry about permutations for orders, but really it's combinations because the orders are built in.
02:03
I've already listed out the orders.
02:05
So this one, two in first, two in second.
02:08
That would be four choose two...