12.) Four teams compete every February in the Beanpot Tournament: Northeastern University, Boston University, Boston College, and Harvard University. In the first round of the Beanpot, two games are played. The winners of those two games then face off in the final. (a) In how many different ways can the teams be matched up for the first round of the tournament? (b) Northeastern and Harvard have never met in the men's Beanpot final. If we assume all four teams are equally likely to make it to the final, what is the probability that, once again, Northeastern and Harvard will not face off in the final in 2023?

12.) Four teams compete every February in the Beanpot Tournament: Northeastern University, Boston University, Boston College, and Harvard University. In the first round of the Beanpot, two games are played. The winners of those two games then face off in the final. (a) In how many different ways can the teams be matched up for the first round of the tournament? (b) Northeastern and Harvard have never met in the men's Beanpot final. If we assume all four teams are equally likely to make it to the final, what is the probability that, once again, Northeastern and Harvard will not face off in the final in 2023?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

At a county fair, you pay $2 to play the following game: You are given a fair coin, and two bags standin front of you, labelled Bag A and Bag B. You flip a coin: If your coin lands Heads, you pick a ballfrom Bag A. If your coin lands tails, you pick a ball from Bag B. Each ball has a dollar value written onit, and you win the number of dollars shown on the ball. • Bag A contains four (4) balls in total: Three (3) balls show $1, and one (1) ball shows $5.• Bag B contains three (3) balls in total: Two (2) balls show $2, and one (1) ball shows $3.You WIN money if you leave with more money than you started with. You LOSE money if you leavewith less money than you started with. You BREAK EVEN if you leave with the same money that youstarted with.Let H denote the event that you flip heads, T denote the event that you flip tails, W the event that youwin, and L the event that you lose.(i) You pay to play exactly one game. What is the probability that you WIN given thatyou flipped a Heads?(ii)…
At a elementary school graduation party 4 girls, 2 boys, and 1 teacher have to be arranged in a row. In how many ways can this be done if: (a) they can be arranged in any order? Answer: (b) the boys must be together and the girls must be together? Answer: (c) the boys must be together but the others can be arranged in any order? Answer:
The following problem is solved by using factors and multiples and features the strategies of guessing and checking and making an organized list. Problem A factory uses machines to sort cards into piles. On one occasion a machine operator obtained the following curious result. When a box of cards was sorted into 7 equal groups, there were 6 cards left over; when the box of cards was sorted into 5 equal groups, there were 4 left over; and when it was sorted into 3 equal groups, there were 2 left. If the machine cannot sort more than 200 cards at a time, how many cards were in the box?
A new game is being introduced at the Hard Rock Cafe. A ball is spun around a wheel until it comes to rest in one of many spots. Whatever is listed in that spot will be the player's winnings. If the wheel has 15 spots labeled $1, 9 spots labeled $2, and 9 spots labeled $10, how much should a player expect to win on average?
Mrs. Smith has 6 activity tables she wants to line up side by side in her classroom. (a) In how many ways can she arrange all 6 tables? Show your work.(b) If she only wants to have 4 of the tables set up, in how many ways can she choose the tables shewishes to have set up? Show your work. Answer:
A new game is being introduced at the Hard Rock Cafe. A ball is spun around a wheel until it comes to rest in one of many spots. Whatever is listed in that spot will be the player's winnings. If the wheel has 8 spots labeled $1, 16 spots labeled $2, and 1 spots labeled $10, how much should a player expect to win on average?
During a special promotion, a customer purchasing a computer and a printer is given a choice of 3 free software packages. There are 10 different software packages from which to select. How many different groups of software packages can be selected? Hint: This is a Combination problem! 120 604,800 360 720
You are planning to plant one durian, one rambutan, one mango and one avocado tree in your garden. The nursery recommends two varieties of durian, four of rambutan, six of mango and three of avocado. (i) How many possible different groups of trees could you plant? If you have already decided on the avocado, how many choices are left for the other trees? (ii)
A new game is being introduced at the Hard Rock Cafe. A ball is spun around a wheel until it comes to rest in one of many spots. Whatever is listed in that spot will be the player's winnings. If the wheel has 11 spots labeled $1, 10 spots labeled $2, and 5 spots labeled $10, how much should a player expect to win on average?
5. Divide and conquer. You're again facing your friend, Brenda, in a "candy-off” game involving a pile of 100 caramels and the winner's prize: one peppermint patty. (Like before, you still LOVE peppermint patties!). On their turn, each player can remove a
Toward the end of a game of Scrabble you hold the letters D,O,G and Q. You can choose three of these four letters and arrange them in order in how many different ways?
(Note that an Ace is considered a face card for this problem) In drawing a single card from a regular deck of 52 cards we have: (a) P( Queen and a 3) = (b) P(black or a 3) = (c) P( black and a Queen ) =. (d) P( face card or a number card) (c) P( black and a face card ) = =