The content is a bit confusing, but this is what you need to focus on -

- You are selecting
`6`

**unique** numbers between 1 to 49
- We are trying to find the probability that out of those
`6`

, **exactly** `5`

are winning numbers.

Now, when we select `6`

numbers, we can have something like - `1, 2, 3, 4, 5, 6`

Now, out of these `6`

numbers, how many `5`

number combinations can we have? We select `5`

numbers from the above `6`

and can get the following -

```
1. (1, 2, 3, 4, 5)
2. (1, 2, 3, 4, 6)
3. (1, 2, 3, 5, 6)
4. (1, 2, 4, 5, 6)
5. (1, 3, 4, 5, 6)
6. (2, 3, 4, 5, 6)
```

That seems straightforward enough. Based on the above, we can see that if we select **any** `6`

numbers, and if we wanted to find out combinations of `5`

from those `6`

, we will **always** get `6`

combinations. Thatâ€™s what the `"6 choose 5"`

gives us.

Letâ€™s go back to the two points I shared in the beginning -

- You are selecting
`6`

**unique** numbers between 1 to 49
- We are trying to find the probability that out of those
`6`

, **exactly** `5`

are winning numbers.

Looking at the 2nd point, letâ€™s assume that `1, 2, 3, 4, 5`

are our `5`

winning numbers. We fix that as an example. As per the 1st point, we still need a 6th number, though. Since we have fixed 1 to 5, we can only select from 6 to 49.

Thatâ€™s what the next part of the content explains us. So, if we fix `1, 2, 3, 4, 5`

as our supposed winning numbers, then we can have the following possible list -

- (
**1, 2, 3, 4, 5,** 6)
- (
**1, 2, 3, 4, 5,** 7)
- (
**1, 2, 3, 4, 5,** 8)
- â€¦
- (
**1, 2, 3, 4, 5,** 47)
- (
**1, 2, 3, 4, 5,** 48)
- (
**1, 2, 3, 4, 5,** 49)

The total number of possible combinations above will be `(49 - 6 + 1)`

, that is `44`

.

We will have `44`

possible successful outcomes.

The next part might be even more confusing -

However, we need to leave out the outcome (1, 2, 3, 4, 5, 6) because weâ€™re only interested in outcomes that match *exactly* five numbers, not *at least* five numbers. This means that for each of our six five-number combinations we have 43 possible successful outcomes, not 44.

To clarify, **if** we need to find the probability that **exactly** 5 are the winning numbers, **and** we know that the lottery tickets only take numbers from 1 to 49, then that means that out of those `44`

lists of numbers above, there can be **1 ticket** which might have **all** `6`

numbers as the winning numbers. We donâ€™t want that. We want **exactly** `5`

numbers.

Thatâ€™s why we get `43`

**possible** successful outcomes.

Hopefully, this clarifies it up a bit. Probability is a tricky subject for me as well.