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**1. The problem statement**

In an episode of the TV show "All in the Family", Mike claimed that he could identify different brands of cola by taste alone. He was challenged and presented with three glasses, one filled with Coke, one filled with Pepsi, and one filled with RC Cola. Suppose that Mike really was

*not*able to discriminate among the brands by taste.

**(a)**Find the probability that none of his identifications would be correct.

**(b)**Find the probability of no matches, had there been four brands instead of just the three.

## Homework Equations

This should be solved using basic probability theory.

## The Attempt at a Solution

By counting combinations, I have found 1/3 in (a) and 3/8 in (b), but can anyone come up with a clever, intuitive way of solving this?

Thanks.