(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Lottery Combinations

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