# Lottery probability

1. Apr 21, 2012

### bartowski

thanks for helping :)

Last edited: Apr 21, 2012
2. Apr 21, 2012

### oleador

Think about this as follows: how many ways are there to choose 2 numbers from 18? (no replacement, order doesn't matter)

3. Apr 21, 2012

### bartowski

i was thinking about this:

numerator: 18C2, 18C2, 19C2 --- but i'm not sure if you ADD or MULTIPLY these
denominator: 55C6

4. Apr 21, 2012

### Dickfore

$$\frac{C^{2}_{18} \, C^{2}_{18} \, C^{2}_{19}}{C^{6}_{55}}$$

Wolfram Alpha

This looks terribly high?!

5. Apr 21, 2012

### bartowski

i was thinking of that.
if you add it on the other hand, its too low

i'm not quite sure with my solution
:(

Last edited: Apr 21, 2012
6. Apr 21, 2012

### Dickfore

No, but this not a probability ot win! This is just a fraction of the total number of outcomes that satisfy your condition. It doesn't mean that if you fill A ticket satisfying this condition that you have this probability to win.

7. Apr 21, 2012

### bartowski

so you think the solution is right? :)

8. Apr 21, 2012

### Dickfore

Yes. The solution is correct.

9. Apr 21, 2012

### bartowski

thanks! :)

10. Apr 21, 2012

### oleador

The intuition for why you have to multiply the combinations is that for every possible combination, say, in [1,18] you can have 18C2 of combinations in [19,36] and 19C2 in [37,55].

11. Apr 21, 2012

### bartowski

now i understand. thanks! :)

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