00:03
We're asked to answer a question about the powerball lottery game using counting principles.
00:12
So powerball, which is a lottery game operated and played in 42 states.
00:20
The game is played by drawing five white balls out of a drum of 59 white balls.
00:39
These white balls are numbered 1 through 59.
00:42
And one red powerball out of a drum of 35 red powerball.
01:02
And these are numbered, of course, 1 through 35.
01:06
We're told that the jackpot is won by matching all five white balls in any order and the red powerball.
01:15
In part a, we're asked to find the possible number of winning powerball numbers.
01:36
So we'll break this up into two stages.
01:40
So the first event is the drawing of the white balls.
01:45
When we draw these white balls, we don't care about the order in which they're drawn, but we do care that we don't draw with replacements.
01:55
So draw without replacement.
02:03
In other words, we're looking for 59 choose five.
02:11
Now by the fundamental property of counting, the total number of winning powerball numbers is the number of combinations of 59 white balls taken five at a time, times, and then we only choose one red powerball out of the 35, so times the number of combinations of 35 red power balls taken one at a time.
02:47
Of course, this is the same as just 35.
02:54
Now, this is a very large number...