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Counting
4. Probability / Counting / Problem 3
Problem 3

In a raffle game, each participant buys a $1\$1 ticket and chooses 44 different numbers from 11 to 6060, without replacement. To win, a participant must select the exact same 44 numbers (order does not matter) that are drawn.
Given that there are 487,635487,635 possible combinations, what should the prize amount be to ensure an average profit of 50%50\%, which is typical for raffles?