# Thread: Pick 6; Match 4

1. ## Pick 6; Match 4

Just needed somebody to verify this

In the pick-6 lottery involving the numbers 1-40, you win the Match-4 prize if exactly four of your six numbers appear on the winning ticket. In a given lottery drawing, how many different tickets would win the Match-4 prize?

$\displaystyle \left(\left({6\atop 4}\right)\right)$ = $\displaystyle \left({6+4-1\atop 4}\right)$ = 126

Thanks

2. Originally Posted by oldguynewstudent
Just needed somebody to verify this

In the pick-6 lottery involving the numbers 1-40, you win the Match-4 prize if exactly four of your six numbers appear on the winning ticket. In a given lottery drawing, how many different tickets would win the Match-4 prize?

$\displaystyle \left(\left({6\atop 4}\right)\right)$ = $\displaystyle \left({6+4-1\atop 4}\right)$ = 126

Thanks
No, I don't think that is correct.

There are $\displaystyle \binom{6}{4}$ ways to pick the matching 4 numbers, and there are $\displaystyle \binom{34}{2}$ ways to pick the non-matching numbers. So...

3. Originally Posted by awkward
No, I don't think that is correct.

There are $\displaystyle \binom{6}{4}$ ways to pick the matching 4 numbers, and there are $\displaystyle \binom{34}{2}$ ways to pick the non-matching numbers. So...
You are correct. Thank you. I'm still trying to get the hang of this.