Counting Problem, Why is this difficult

[IronWing]

Just make a chart of all the combinations and add them up. Sometimes there is no substitute for brute force.

 

[us3rnotfound]

Simple to think about this way. Each cookie is distributed independently.

How many ways are there to distribute just one cookie among 10 kids, assuming you're not going to break the cookie into halves, or quarters, or crumbs, etc., which leads to an incredibly high number of ways, although not infinite as some people might claim. The reason for there not to be an infinite number of possible distributions is that you can only divide a cookie into a finite number of pieces. Even if you divide it into its constituent atoms, that's still a finite number.

Anyway, there are 10 ways to distribute 1 cookie.

How many ways are there to distribute another cookie? 10 ways.

Since they're independent of each other, you can use the counting principle: 10 *10 ways to distribute 2 cookies.

Likewise, 10 * 10 * 10 * . . . * 10 i.e. 10^20
OP is correct, this is the explanation.

Nice, exactly what I was looking for, thanks! :thumbsup;