Solution Found!
A round-robin tournament is being held with n tennis players; this means that every
Chapter 1, Problem 4(choose chapter or problem)
A round-robin tournament is being held with n tennis players; this means that every player will play against every other player exactly once.
(a) How many possible outcomes are there for the tournament (the outcome lists out who won and who lost for each game)?
(b) How many games are played in total
Questions & Answers
QUESTION:
A round-robin tournament is being held with n tennis players; this means that every player will play against every other player exactly once.
(a) How many possible outcomes are there for the tournament (the outcome lists out who won and who lost for each game)?
(b) How many games are played in total
ANSWER:Step 1 of 2
(a)
There are n tennis players, thus the number of games played in total is given by the combinatorial formula:
\(C(n, r)=\frac{n !}{(n-r) ! r !}\)
Here r = 2,
Therefore, the total number of games played is :
\(C(n, 2)=\frac{n !}{(n-2) ! 2 !}\)
Since each game has two outcomes, the number of possible outcomes for the tournament is :
\(2^{C(n, 2)=2^{\frac{n !}{(n-2) ! 2 !}}}\)