How many different winning lottery tickets?

boo143

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Question - The Powerball lottery is decided every Wednesday and Saturday night by drawing five white balls out of a drum with 69 balls and one red ball out of a drum with 26 red balls. The Powerball jackpot is won by matching all five white balls in any order and the red Powerball. Each ticket costs $2.

a. How many possible different Powerball tickets can be purchased?
b. How many possible different winning Powerball tickets are there?


  1. I got the answer for a by multiplying 69C5 by 26C1 to get 292,201,338. I am stumped on how to calculate b. I'm thinking it would be 6x5x4x3x2?
    Please help!



 
Question - The Powerball lottery is decided every Wednesday and Saturday night by drawing five white balls out of a drum with 69 balls and one red ball out of a drum with 26 red balls. The Powerball jackpot is won by matching all five white balls in any order and the red Powerball. Each ticket costs $2.

a. How many possible different Powerball tickets can be purchased?
b. How many possible different winning Powerball tickets are there?


  1. I got the answer for a by multiplying 69C5 by 26C1 to get 292,201,338. I am stumped on how to calculate b. I'm thinking it would be 6x5x4x3x2?
    Please help!



Well let's see. If you can buy a Powerball ticket with 6 numbers, then this ticket could be a winning ticket. Now if they draw 6 numbers then you could have purchased a ticket with those same numbers. This is all that you need to get the answer to part b.
 
The exercise statement confused me, the first time I read it. They refer specifically to "the powerball jackpot" and then ask in part b) how many winning combinations are possible for a single drawing. It's not actually a trick question (asking about the big jackpot only), agree?

I understand winning combinations don't need to be "the powerball jackpot", but I'm ignorant about other winning categories. If a person picks two correct numbers, does that generally count as a winner? Maybe you need three numbers, to win something. (I don't gamble at the lottos.)

I agree with your reasoning and answer for part a). :cool:
 
Question - The Powerball lottery is decided every Wednesday and Saturday night by drawing five white balls out of a drum with 69 balls and one red ball out of a drum with 26 red balls. The Powerball jackpot is won by matching all five white balls in any order
a. How many possible different Powerball tickets can be purchased?
b. How many possible different winning Powerball tickets are there?
  1. I got the answer for a by multiplying 69C5 by 26C1 to get 292,201,338. I am stumped on how to calculate b. I'm thinking it would be 6x5x4x3x2?
There are \(\displaystyle \dbinom{69}{5}\cdot\dbinom{26}{1}=280962825\) SEE HERE
Why would you think the answer to a. is different from b. ?
Is it possible that you have failed to tell us of other ways to have a winning combination?
 
The exercise statement confused me, the first time I read it. They refer specifically to "the powerball jackpot" and then ask in part b) how many winning combinations are possible for a single drawing. It's not actually a trick question (asking about the big jackpot only), agree?

I understand winning combinations don't need to be "the powerball jackpot", but I'm ignorant about other winning categories. If a person picks two correct numbers, does that generally count as a winner? Maybe you need three numbers, to win something. (I don't gamble at the lottos.)

I agree with your reasoning and answer for part a). :cool:



First, I thought that it was a trick question, and that the answer was just 1. Then, I thought it would be the same answer as part a). Then I thought that even if you match just two numbers, you still win something, hence a winning ticket. My instructor used this example: "Think of it this way - pretend the winning numbers are 2,4,5,6,7 and a powerball of 20. How many different winning tickets are possible?"
Apparently, the answer is 1 which I still don't understand because it is possible that more than one person could select the exact same numbers in order to split the jackpot. Therefore, there could be more than 1 winning ticket.
I want to pull my hair out.
 
… My instructor used this example: "Think of it this way - pretend the winning numbers are 2,4,5,6,7 and a powerball of 20. How many different winning tickets are possible?" Apparently, the answer is 1 …
Then it is a trick question. There's only one winning combination possible per drawing for "the powerball jackpot". (Duh, right?)
 
I can't post the rest of my reply; I keep getting 500 Infernal Server Error messages. I'll try sentence-by-sentence …
 
… I still don't understand because it is possible that more than one person could select the exact same numbers in order to split the jackpot.
Yes, but that interpretation is not possible to answer.
 
There's no way to know the number of duplicated combinations purchased, for any given drawing, until after sales have closed, and this number would not be constant from drawing to drawing, anyway. The exercise also doesn't specify what constitutes a winning ticket, other than for "the powerball jackpot", so that must be the winning combination they're talking about. (I think part b is poorly worded, I don't understand the point in asking, and I'd move on.)

Yay, this time it only took five attempts to post, and I wasn't logged off for 20 minutes. :roll:
 
There's no way to know the number of duplicated combinations purchased, for any given drawing, until after sales have closed, and this number would not be constant from drawing to drawing, anyway. The exercise also doesn't specify what constitutes a winning ticket, other than for "the powerball jackpot", so that must be the winning combination they're talking about. (I think part b is poorly worded, I don't understand the point in asking, and I'd move on.)

Yay, this time it only took five attempts to post, and I wasn't logged off for 20 minutes. :roll:

I agree, and I argued that!!!! He said I was overthinking the question, but I feel it is terribly worded which made me lose hours worth of valuable other stuff time!!!!
 
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yeah but couldn't multiple people have the same numbers?
Yes!, but still there is just ONE set of 6 numbers that will make you (and possibly others) a winner. That is how someone can say the answer is 1.

On the other hand 23 people or 11 people or just 1 person can have the winning numbers, so the answer is 23 or 11 or 1 or .... This means there is no answer.

As a result I think the answer is 1 and that the problem was maybe not worded 100% correctly. Learning how to read a prob. problem is an art!
 
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In posts #11 and #12, it looks like you transposed your responses to the quotes, maybe?

Yes, it's possible to have two Powerball winners, or three, or four, or …. how would you know when to stop counting this way? Common-sense guesstimate? Or, go all the way to "mathematically feasible"?

The question seems ambiguously worded; I'm not sure what the point is. No matter how I parse it, the answer is either obvious or nuts.

You may report something like the following; otherwise, I don't think I can help any further. :cool:

Winning tickets do not exist until after a drawing; there is only one winning combination possible for any particular Powerball Jackpot.

If the question's intent is to be global, as in how many different winning tickets (combinations) can possibly exist were this game to be played sufficiently long for every possible combination to occur and at least one ticket was purchased for each of them, then the answer to part b) is the same as the answer to part a).
 
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