# Lottery Combinations

1. Oct 4, 2011

### jumbogala

1. The problem statement, all variables and given/known data
Students are playing a lottery game. In this game, three numbers are drawn from a set of six.

If the three numbers on a student's ticket match those drawn, the student wins the full prize. If just one or two numbers match, the student wins a consolation prize.

The order of the numbers doesn't matter. Also, once a number is picked it cannot be picked again.

a) How many tickets would a student have to buy to guarantee that at least one number out of 3 matches the winning combination?

b) What if at least 2 numbers need to match?

c) What if all 3 numbers need to match?

2. Relevant equations

3. The attempt at a solution
a) I know that the answer to is 2 tickets. This is because you could buy the following:

1,2,3 on one ticket. 4,5,6 on the other. This way, at least one of the numbers will match the winning ticket.

But I have to represent this mathematically. Would it be (6 choose 1) / 3?

b) If my formula is correct, then it would be (6 choose 2) / 3

c) (6 choose 3) / 3

But I am not sure if my formula is right. I'm having trouble reasoning it out in my head.

2. Oct 5, 2011

### boaz

It seems fine to me, except the last one. In general, you get the total number of combinations and divide it by the number of winning combinations in each ticket, as a result you get the number of tickets.

For instance, in the 2nd question, we have C(6,2) combinations. However, each ticket has 3 combination (because if we have x,y,z then (x,y), (y,z) and (x,z) are winning combinations). However, in the 3rd question we have C(6,3) but each ticket covers only one winning combination.

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