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I might recommend coin tossing as a topic, which is somewhat combinatoric-y? Two examples. First, "spinning a penny instead of tossing it results in heads only about 30% of the time" (MathWorld, from Paulos). This should be detectable in an experiment run with the group, and would be quite surprising.

Second, the expectations of runs (consecutive Heads or consecutive Tails) of different lengths are distinctive enough so that it is possible to reliably distinguish between a true random sequence and a "fake" random sequence. Ask them to both write down strings of H's and T's, and generate truly random strings from coin flipping, without revealing which to you. Then you magically uncover which are real and which not. This idea is due to Pál Révész. See his "Strong theorems on coin tossing" (PDF). See also Mark Schilling's "The longest run of heads" (PDF). You could connect this to discrepancy theory to show it is not just play.

Then you could mention the recent Diaconis-Holmes-Mongomery work on "Dynamical bias in the coin toss" (PDF).

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I might recommend coin tossing as a topic, which is somewhat combinatoric-y? Two examples. First, "spinning a penny instead of tossing it results in heads only about 30% of the time" (MathWorld, from Paulos). This should be detectable in an experiment run with the group, and would be quite surprising.

Second, the expectations of runs (consecutive Heads or consecutive Tails) of different lengths are distinctive enough so that it is possible to reliably distinguish between a true random sequence and a "fake" random sequence. Ask them to both write down strings of H's and T's, and generate truly random strings from coin flipping, without revealing which to you. Then you magically uncover which are real and which not. This idea is due to Pál Révész. See his "Strong theorems on coin tossing" (PDF). You could connect this to discrepancy theory.

Then you could mention the recent Diaconis-Holmes-Mongomery work on "Dynamical bias in the coin toss" (PDF).