2001 AMC 12 Problem 16
Below is the professionally curated solution for Problem 16 of the 2001 AMC 12, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2001 AMC 12 solutions, or check the answer key.
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Difficulty rating: 1600
16.
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?
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.
Problem 16 in Other Years
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