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Choosing Stuff.md

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+#Math #Probability
+
+# 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:
+
+ 
+
+$$
+{m + n} \choose {l + o}
+$$
+
+Total ways to choose $l$ items of type one: 
+
+$$
+m \choose l
+$$
+
+Total ways to choose $o$ items of type two: 
+
+$$
+n \choose o
+$$
+
+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: 
+
+$$
+\frac {{m \choose l} {n \choose o}} {{m + n} \choose {l + o}}
+$$