math

At the first meeting of the chess club, the 10 members decided that everyone in the club should play everyone else one time to determine the best players for the inter-school competitions. How many games had to be played?

  1. 👍 0
  2. 👎 0
  3. 👁 412
  1. Same as the standard "hand-shake" problem
    number of games = 10 choose 2
    = C(10,2) = 45

    In the hand-shake problem, we have 10 people and they all shake hands on meeting.
    so each of the 10 people can shake hands with 9 others for 90 shakes
    but that would include A shaking with D and D shaking with A, the same handshake, so we divide our 90 by 2 to eliminate all duplicate pairs.
    The same argument applies to your players
    Player A vs B is the same game as B vs A

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. History

    Which option most accurately describes the purpose of the Council of Trent? it was a meeting called by Pope Paul 111 to address reformation issues such as the selling of indulgences, clerical corruption, and other abuses it was a

    asked by malia on October 16, 2017
  2. Math

    A certain club has 50 people, and 4 members are running for president. Each club member either votes for one of the 4 candidates, or can abstain from voting. How many different possible vote totals are there?

    asked by St3v3 on June 15, 2020
  3. Algebra

    A club currently has 300 members who pay $ 400 per month for membership dues. The​ club's board members want to increase monthly revenue by lowering the monthly dues in hopes of attracting new members. A market research study

    asked by Janice on June 24, 2015
  4. math

    The mathematics club in a school has 53 members. 5/7 of the girls members and 3/5 of the boys members are from lower secondary. The total number of lower secondary members is 35. How many members of the club are boys?

    asked by Waqas on September 4, 2016
  5. Math

    Challenger elementary school has 800 students every Wednesday 12% of the students stay after school for chess club how many students attend chess club on Wednesdays

    asked by Anonymous on July 29, 2019
  1. Combinations and Permutations

    A committee of 3 members is selected from a club made up of 10 junior members and 20 senior members. What is the expected number of juniors in the committee?

    asked by Charles on October 4, 2015
  2. Pre-Algebra

    A chess club with 40 members is electing a new president. Lisa received 16 votes. What percentage of the club members voted for Lisa?

    asked by Anonymous on September 18, 2016
  3. math

    The local reader’s club has a set of 36 hardback books and a set of 30 paperbacks. Each set can be divided equally among the club members. What is the greatest possible number of club members?

    asked by NUNYA on October 11, 2017
  4. History

    Which option most accurately describes the purpose of the Council of Trent? it was a meeting called by Pope Paul 111 to address reformation issues such as the selling of indulgences, clerical corruption, and other abuses it was a

    asked by malia on October 16, 2017
  5. Algebra

    The school photography club charges $10 for each photo in its annual pet photo contest. The club wants to save $75 of its earnings for a pizza party. The club members also want to have at least $50 left over after the pizza party

    asked by Katelyn on October 19, 2017
  6. mathematics

    A chess club with members is electing a new president. Aldo received votes. What percentage of the club members voted for Aldo?

    asked by Aldo on May 12, 2020

You can view more similar questions or ask a new question.