# Thread: Basic Probability Has Me Stumped

1. ## Basic Probability Has Me Stumped

Hey everyone,

So I feel stupid, but I just can't figure this out. I have an exam tomorrow and one of the practice questions is as follows; it's broken into two parts:

Part One:

To play the Cash 5 lottery you must select 5 different numbers from a field of numbers from 1 - 40. Calculate your chances of winning the jackpot; getting 5 out of 5 correct.

This one was simple enough

40 x 39 x 38 x 37 x 36
--------------------- = 658,008
5!

So it's a 1:658,008 chance of winning. Simple enough.

Now part two asks the chances of getting 4 out of 5 correct. This has me stumped... I know it should work out to 1:3,760 but I cannot figure out how... If someone could help I'd greatly appreciate it.

Thanks in advance

2. We are choosing 4 from the 5 winning balls and 1 from the other 35 which are not winners.

$\displaystyle \frac{C(5,4)\cdot C(35,1)}{C(40,4)}$

BTW, for the first one, odds would be 1:658007

You win once for every 648007 times you lose.