OK - a probability question for everyone. I have 4 random numbers between 1 and 8.?

Question

What are the odds that they will equal 21? 4 numbers, each number can only be 1 through 8, but some numbers will repeat.

This is for a game we are planning in our call center called "21's" based on confirmation numbers they generate after a sale. If they add the four numbers up and they equal 21 they get a prize. I need to quote what the odds of winning are. So maybe this is really an odds question.

Answer 1

You need to calculate all combinations that add up 21 and divide it by 8*8*8*8

An excel table will work out.

Answer 2

I calculated the odds out longhand and found the odds to be 6.93%.

There are 4096 possible combinations of numbers. 284 of these combinations add up to 21.

Answer 3

i apologize i did my math wrong.

284/4096 reduces to 71/1024

i removed the 9's from my first go but forgot about the 0's.

if you really want me to explain my process (and my pain) as to how i came up with that answer i will...  but i spent too much time on it ;)

Edit:  You got me there James.  It is 6.93 percent.  But then its not odds is it?