00:01
In this problem, we need to determine the probability of winning a lottery.
00:06
Now, in the first subpart, it is said that we need to find the probability of selecting the five winning numbers from 1 -2 to 31.
00:15
Now, the question also says that the numbers selected will be different and the order does not matter.
00:21
So, the probability will be the number of favorable outcomes divided by the total number of outcomes.
00:27
Since there is only going to be one winning ticket, so that means that the number of favorable outcomes will be one.
00:34
As for the total number of outcomes, that will be the number of ways in which we can select five numbers from 1 to 31 without considering the order.
00:44
That means out of 31 numbers, we need to select five numbers.
00:49
And since the order does not matter, this can be done in 31c5 ways.
00:53
C represents combination.
00:55
So we have a number.
00:56
So we have 1 divided by 31c5.
00:58
31c5 is 31 factorial divided by 5 factorial times the factorial of 31 minus 5, which is equal to 26.
01:08
So if we calculate that, then in the denominator we will get 169911...