通过计算概率得出整除性

hbghlyj

IMO 1972, Problem 3.
关于@Jack D'Aurizio的回答：

Every subset of $n$ politicians in the left wing has the same probability to be part of the super-committee, and
$$ \binom{n+m}{n}\mid \binom{2n}{n}\binom{2m}{m} $$
also comes from computing the probability for a single politician to be part of the super-committee.

没看懂概率是怎么算的。也没看懂如何通过计算概率得出整除性

AoPS、MSE有其它证明。

hbghlyj

@Mike Spivey的回答
there is no known combinatorial interpretation of the numbers $$A(m,n) = \frac{(2m)! (2n)!}{m! n! (m+n)!}.$$

据此推测1# @Jack D'Aurizio的回答是錯的？