00:01
In its question, when given the california super lotto plus, players pick 5 different numbers from 1 to 47 and separately pick a mega number from 1 to 27.
00:13
Take note that since different numbers are picked, they are picked without replacement.
00:23
After picking, there is no particular arrangement or order to the numbers picked, so the order is not important.
00:30
But without replacement order, not important, we'll be using combination.
00:42
That's the one we see.
00:45
So in part a, we want to find probability of matching all five of the numbers you pick to the five winning numbers and also match the mega number you pick to the winning mega number.
00:59
So that would be, we know that there's only one set of five numbers that are the winning numbers.
01:05
Out of, in probability, we always want to divide by the total number of possible ways in this case to pick five numbers with no restriction.
01:16
And that is to take from the 47 numbers, we want to choose five of them.
01:22
Choose because we're using combination.
01:24
N.
01:26
Now, n in probability in combinatorics is times or is plus.
01:31
So n, there's a times.
01:34
For the mega number to match the mega number, there's only one winning mega number out of 27 possible mega numbers.
01:46
And so that would be 1 out of 1533 -9 -9 -tri -9 comes 1 out 27.
02:01
And that will be 1 out of 4141 -6353, which is approximately 0 .000000 -0 -000 -0 -0 -0 -0 -0 -0 .000...