00:01
Okay, this problem says, in one lottery game, contestants pick five numbers from 1 through 40 and have to match all five for the big prize, but the numbers can be in any order.
00:15
What's the probability you'll win if you buy one ticket? hint, your chances are not good.
00:22
Okay, since the order does not matter that we're choosing them, we're going to choose, we're going to use combinations because the order doesn't matter.
00:32
There are 40 different numbers and we've got to choose five of them.
00:39
Now, the formula for combinations, the combination of n taking r is n factorial over r factorial and then n minus r factorial.
00:53
Factorial just means you start with that number and you multiply all the way down till you get through times one.
01:00
So, for this one, i would have 40 factorial over 5 factorial and then 40 minus 5 is 35 factorial.
01:12
Okay, let me erase this one where i'll have more room to work.
01:17
All right, 40 factorial means 40 times 39 times 38 times 37 times 36 times 35 all the way down till i get to times one over 5 factorial is 5 times 4 times 3 times 2 times 1 and then times 35 factorial is 35 times 34 times 33 times all the way down till i get to one.
01:50
Do you see that 35 times 34 times 33? that's in both of them, top and bottom.
01:57
So, i'm going to cancel out from 35 on down.
02:02
Okay, now, if i take 5 times 4 times 2, that's 40.
02:11
So, i'm going to mark that one out.
02:14
For 3, i'm going to divide 3 into 36 and get 12...