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2020 PUMaC Combinatorics A2 / B3

Source:

January 1, 2022
combinatorics

Problem Statement

Cary has six distinct coins in a jar. Occasionally, he takes out three of the coins and adds a dot to each of them. Determine the number of orders in which Cary can choose the coins so that, eventually, for each number iāˆˆ{0,1,...,5}i \in \{0, 1, . . . , 5\}, some coin has exactly ii dots on it.
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