A lottery is set up so that each player chooses six different numbers
from 1 to 15.  If the six numbers match the six numbers drawn randomly
in the lottery, the player wins the top cash prize.  What is the
probability of winning the prize with 1 ticket?

What I have so far:
15c6=15!/(15-6)!6!=2,594,592,000

My answer is 1 in 2,594,592,000 to win the cash prize with 1 ticket.

I want to make sure that is correct.

Hi unknownentity-ga,

Your approach is correct, however the calculation is not.

Your intuition that your chances of winning this lottery is the
inverse of the number of ways to choose any six numbers out of 15,
without repeats.

The MathWords site has more information on the combinations formula
you were trying to use:

http://www.mathwords.com/c/combination_formula.htm

Applying the formula:

n C r = n!/r!(n-r)!

15 C 6 = 15!/6!9! = (1307674368000)/(261273600)= 5005

So the chance of winning with a single ticket is 1/5005, or roughly 0.02%.

Hopefully that clears things up - thanks for using Google Answers.

Cheers!

answerguru-ga

You're brilliant. :-)

I cant believe that someone actually paid $10.00 for this. I learnt
this in like 6th form or Year 12.