00:01
All right, here we are asked that if a presidential candidate plans to begin her campaign by visiting the capitals in three out of 49 states, so three of 49 states, what is the probability that she selects the root of three specific capitals? well, excuse me, the first thing we're going to do is say, how many ways can we choose three out of 49 states? that's going to be 49 choose three.
00:28
Now, we're going to use our formula for combinations to do this.
00:32
So this is going to be 49 factorial over now 3 minus or 49 minus 3, which is 46 factorial and then 3 factorial.
00:43
So this is going to simplify into 49 times 48 times 47 over 3 times 2 times 1.
00:53
And that's because everything from 46 down cancels out of the numerator.
00:58
So we're left with 3 times 2 times 1.
01:01
Now this is equal to 6, and 6 goes into 48 8 times.
01:06
So the number of ways of picking these 3 states is going to be 49 times 8 times 47...