# Math Help - Combinatorics problem

1. ## Combinatorics problem

The problem is a lottery problem. For the Mega Millions drawing, the official website says that there is a 1 in 306 chance of getting 3 out of the 5 regular numbers correct without matching the mega ball. The prof wants to see how we calculate this. I am stuck and getting nowhere near 306.

This is where I am at...

To figure out all the possible combinations of the 5 regular numbers is :

C(56,5) which is 3819816

from here I am lost

2. Hello minkyboodle
Originally Posted by minkyboodle
The problem is a lottery problem. For the Mega Millions drawing, the official website says that there is a 1 in 306 chance of getting 3 out of the 5 regular numbers correct without matching the mega ball. The prof wants to see how we calculate this. I am stuck and getting nowhere near 306.

This is where I am at...

To figure out all the possible combinations of the 5 regular numbers is :

C(56,5) which is 3819816

from here I am lost
For those of us not familiar with the Mega Millions lottery (this Forum has members all over the world!), it would help if you stated clearly what 'getting 3 out of the 5 regular numbers' means. You may even find that, in providing us with an exact formulation of the problem, you realise for yourself how to solve it.

3. you have to pick 5 numbers from 1-56

4. Hello minkyboodle
Originally Posted by minkyboodle
you have to pick 5 numbers from 1-56
Yes. This can be done in $\binom{56}{5}$ ways. And then what?

5. I already know that the odds of getting 3 out of 5 is 1/306. I am just trying to do the proof and I am struggling to set it up.

6. I am going to try and re-word everything.

in the lottery, the lottery people pick 5 numbers from 1-56. The odds of someone matching 3 of those 5 selected numbers is 1/306. How do we get there?

7. Hello minkyboodle

I've just been doing some research into your Mega Millions lottery. You didn't say anything about the Mega Number - which (so I have discovered) does not have to match any of your numbers, and must figure in the calculation.

You'll find the way the odds are calculated to give the 1 in 306 result just here. (Scroll down until you reach the paragraph for Payout = \$7.)