Ask a Mathematician

[polymath257]

OK, I'll take you through one of the problems. The rest are done in a similar way.

First, there are 35 odd and 34 even numbers between 1 and 69. There are 13 odd and 13 even numbers between 1 and 26.

So, suppose you want 3 odd numbers and 2 even numbers between 1 and 69. I assume that order doesn't matter and no number can be repeated.

Then, there are 35*34*33 *ordered* ways to pick 3 odd numbers. Divide this by 3*2*1 ways of permuting those and we get 35*34*33/(3*2*1) ways to pick 3 even numbers between 1 and 69.

For the even, you will have 34*33/(2*1) possible ways.

Multiply these two numbers to get the total number of ways of picking 3 odd and 2 even numbers from 1 to 69:

(35*34*33/(3*2*1) * 34*33/(2*1) = 3561745 ways of picking white balls in this scenario.

You still need to pick the red balls, and if you only pick one, there are 26 ways t . So multiply
all together to find

3671745*26=9546370 ways.

This, by the way, will be the same as picking 3 balls from 35-69 (35 possibilities) and 2 from (1-34) (34 possibilities) and then one red ball.

By the way, this isn't mathematics as it is done today. You could have easily looked up the process online.

Thanks to had take time to answer me !

(35*34*33/(3*2*1) * 34*33/(2*1) I get with my calculator the next result : 3671745 but you get 3561745.
Numbers in bold indicate the different numbers in ours results.

Yes, it is 3671745. I read the calculator wrong. Sorry.