## 5369855 3 years ago In a state lottery, a player fills out a ticket by choosing five "regular" numbers from 1 to 45, without repetition, and one PowerBall number from 1 to 45. The goal is to match the numbers with those drawn at random at the end of the week. The regular numbers chosen do not have to be in the same order as those drawn. How many different ways are there to fill out a ticket?

1. joemath314159

45C5 * 45C1 where: $nCr = \left(\begin{matrix}n \\ r\end{matrix}\right) = \frac{n!}{r!(n-r)!}$ you want to calculate: $\left(\begin{matrix}45 \\ 5\end{matrix}\right)*\left(\begin{matrix}45 \\ 1\end{matrix}\right)$

2. joemath314159

nCr is read "n choose r" Its how many ways you can choose r things from a group of n objects.

3. 5369855

Thank you so much!! :) Big help!

4. 5369855

How would I solve the problem if it said: A player wins the jackpot by matching all five regular numbers plus the PowerBall number. This is called "Match 5+1." How many different ways are there to fill out a ticket that is a "match 5+1" winner? What is the probability of the event "Match 5+1"?

5. joemath314159

The number of ways to fill out the ticket would be the same (assuming there are still 45 numbers to choose from). As for the probability of winning, once you get the answer to the first problem (lets call it CAT for lulz), it would be: $P(winning) = \frac{1}{CAT}$

6. 5369855

so what's the difference between this question and the last one i asked you? there has to be a difference

7. joemath314159

There isnt a difference that i can tell. In the first one you wanted to know how many ways you can fill out a ticket where you have to pick 5 numbers from 45 and one bonus number from 45. Its the same thing in the second problem. You're filling out the same type of ticket.

8. joemath314159

The only way there would be a difference is if you had to match the order of the numbers. Then there is major difference.

9. 5369855

ok but for probability, shouldn't it be a fraction? Ex: 1/4 probability?

10. joemath314159

it will be, the answer will be 1/(some big number), which logically makes sense, because the probability of winning the lottery should be really really low.

11. 5369855

Thanks so much for all your help! :)