2001 AMC 12 Problem 16
Problem 16 of 25IntermediateCounting & Probability
A spider has one sock and one shoe for each of its eight legs. In how many different orders can the spider put on its socks and shoes, assuming that, on each leg, the sock must be put on before the shoe?
Answer choices
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Solution
Think of the items ( socks and shoes) arranged in some order: there are arrangements.
For each leg, the sock comes before the shoe in exactly half of all arrangements. Imposing this on all eight legs independently divides by giving
Thus, the correct answer is D.