2022 CMWMC Guts Round 4/8 - Carnegie Mellon University Womens' Competition
Source:
August 12, 2023
CMWMCalgebrageometrycombinatoricsnumber theory
Problem Statement
Set 4
p10. Eve has nine letter tiles: three ’s, three ’s, and three ’s. If she arranges them in a random order, what is the probability that the string “” appears somewhere in the arrangement?
p11. Bethany’s Batteries sells two kinds of batteries: batteries for per package, and batteries for per package. After a busy day, Bethany looks at her ledger and sees that every customer that day spent exactly , and no two of them purchased the same quantities of both types of battery. Bethany also notes that if any other customer had come, at least one of these two conditions would’ve had to fail. How many packages of batteries did Bethany sell?
p12. A deck of cards consists of cards labeled with the integers to , inclusive. The cards numbered through are purple, and the cards numbered through are green. Lilith has an expansion pack to the deck that contains six indistinguishable copies of a green card labeled with the number . Lilith wants to pick from the expanded deck a hand of two cards such that at least one card is green. Find the number of distinguishable hands Lilith can make with this deck.
PS. You should use hide for answers.