Probability, help needed

I'm trying to solve this easy problem in combinatorics, and i'm stuck. The question is "what are the odds of winning jackpot in lottery '7 of 39' if you can pick 20 numbers. I know that it must be something bigger than when picking only 7 numbers, but don't know how find the answer. I know basic elements of combinatorics and probability, so even a little hint would be useful. Thanks

Not clear on the question: do you mean instead of choosing the normal 7 on one ticket, you get to choose 20, and if 7 of those 20 match the winning numbers, you win?  Or do you mean it's a "20 of 39" ticket?

yes, instead of choosing the normal 7 on one ticket, you get to choose 20, and if 7 of those 20 match the winning numbers, you win. i know it's lame problem, but couldn't get it

The probability of winning = (total number of possible ways to choose the winning number) / (total possible ways to choose 7 of 39 numbers)

The denominator is C(39,7) = 39! / (39-7)! * 7! = 15,380,937.

On a normal ticket, where you just choose 1 set of 7 numbers, the numerator is C(7,7) = 1, giving a probability of winning of 1/15,380,937.  In the case of choosing 20 numbers, the numerator is C(20,7) = 20! / (20-7)! * 7! = 77,520.  And thus the probability of winning by choosing 20 numbers in a 7 of 39 game is 77,520/15,380,937 or about 0.5%

Not bad.

thanks dude. you saved my sanity.