How many league matches were played, write an algebraic expression to
denote the number of
league matches between the teams, if the number of teams is n.
look at the pattern.
Two teams A, B
one game: C(2,2) = 1 ---> from 2 choose 2 for a game
AB
Three teams A,B,C
AB, AC, BC --- three games , C(3,2) --> from 3 choose 2 for a game
Four teams A,B,C,D
AB, AC, AD, BC, BD, CD - 6 games, C(4,2) ---> from 4 choose 2
...
n teams ---- C(n,2) , from n choose two
C(n,2) = n!/(2!(n-2)!)
= n(n-1)(n-2)(n-3)!/(2(n-2)(n-3)!_
= n(n-1)/2
And now "Sweety" or whatever s/he is called is banned for posting filth.
To calculate the number of league matches between n teams, we need to recognize that each team will play against every other team twice (once at home and once away).
Let's break this down step by step:
Step 1: Determine the total number of possible matchups between n teams. This can be calculated using the formula for combinations, denoted as nC2, which represents the number of ways to select 2 teams from a group of n:
nC2 = n! / (2! * (n-2)!)
Step 2: Multiply the number of possible matchups by 2 to account for each team playing both at home and away:
2 * nC2 = 2 * (n! / (2! * (n-2)!) )
= n! / (n-2)!
Therefore, the algebraic expression to denote the number of league matches between n teams would be:
n! / (n-2)!