Here's a question that I'm struggling with:
Jack, John and Tom given 20 brownies by their mom, in a random manner. They are arguing: what are the odds that Jack will get all of them?
Jack says that there are $\binom{20+2}{2}$ different ways to give the brownies, so his chances are $\frac{1}{\binom{20+2}{2}}$
John say that they all have the same chances for each brownie, so the chances are $(\frac{1}{3})^{20}$.
Who is right? I think Jack is wrong because he didn't count similar divisions in which the brownies were given in a different order.
But I think the real issue here is - when do I choose Bernoulli with $\frac{1}{3}$ success chance, and when do I choose a uniform distribution and count all possible divisions?
Thanks!