Question 1023651: If 20 premier league are present and five of the team represent one company the find the number of ways pair of team representing different companies can play a game
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website!
Question:
If 20 premier leagues are present and five of the teams represent one company then find the number of ways a pair of teams representing different companies can play a game.
Solution:
There are C(20,2) different matches of two teams can be made, out of which C(5,2) are from the same company, where C(n,r)=n!/(r!(n-r)!).
So C(20,2)-C(5,2)=190-10=180.
When we solve permutations, we need to look for different ways of looking at the same problem. If the results come up the same, this is a verification, or a combinatorial proof that the two expressions are identical.
Here's another aspect of the same problem.
Assume two cases,
A. the company has no team in the matches.
So there are C(15,2)=15*14/2=105 matches.
B. the company has a team in the matches. Then one particular team of the company can play 15 adversaries, therefore the five teams of the company can form 15*5=75 matches.
Adding the two cases, we have
number of ways = 105+75 = 180 as before.
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