2007/08 AHSMC Part 1 Problem 4

Problem 4 of 16

The number of ways in which five As and six Bs can be arranged in a row which reads the same backwards and forwards is

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Solution

The middle symbol must be an A. The first five symbols consist of two As and three Bs, and they can be arranged in all possible ways. The last five symbols, consisting also of two As and three Bs, must be in reverse order with respect to the first five symbols. In the first five symbols, we only have to find the number of ways of choosing two of the five positions for the two As. This is given by $\dbinom{5}{2} = 10$ . The answer is (C). An exhaustive analysis also works.

University of Alberta

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