Concept
How many ordered outcomes are possible for first, second, and third place?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"To encourage rivalry and gluttony, we’re going to give a special certificate to the child who collects the most candy at the end of the night. And while we’re at it, we’ll give 2nd-place and 3rd-place certificates as well. How many different ways could our 1st-2nd-3rd contest turn out? This is a partial permutation: there are eleven possible winners, and ten possible runners-up for each possible winner, and nine possible 3rd-placers for each of those top-twos. The answer is therefore 11^3, or 990. Wow! I wouldn’t have guessed that high."
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