Problem

Given $m$ items of one type and $n$ items of another type, what is the probability of choosing $l$ items of type one and $o$ items of type two if you pick $l + o$ items?

Solution

Total ways to choose the items not considering types:

(l + o m + n)

Total ways to choose $l$ items of type one:

(l m)

Total ways to choose $o$ items of type two:

(o n)

Multiply the ways to choose both items to get the number of ways to choose $l$ items of type one and $o$ items of type two, divide by total number of combinations:

\frac{( l m ) ( o n )}{( l + o m + n )}

@craisin's notes

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