Abstract: Suppose you are having a party and want to ensure that you have a group of n guests each of whom has met the other members of the group of n before or a group of n guests none of whom has met the other members of the group of n before. What is the smallest number of people you can invite to your party while ensuring that this occurs? While the actual answer to this question is not known for n larger than 4 (yes, four!), it is possible to show that you need at least 2^(n/2) guests. However, the proof does not produce a party with fewer guests that fails to have the desired property, it uses probability to show that such a configuration of guests exists.

The above result due to Paul Erdos is just one example of many fundamental yet accessible results in combinatorics that use probability (and rather elementary probability at that) to answer a question that doesn't involve probability in any way. In this talk, we will survey several intriguing results of this type. No knowledge of combinatorics or probability is required, as we will introduce ideas as we need them.