Q. A set of football matches is to be organized in a "round-robin" fashion, i.e., every participating team plays a match against every other team once and only once. If 21 matches are totally played, how many teams participated?

• This problem is similar to handshaking problem...
  So by the concept of Combination we can say that
  nc2=21
  or,n*(n-1)=42 now just put n=7 then satisfy the equation...
  So simply There was 7 team....Thank You :)
• 10 years agoHelpfull: Yes(13) No(1)
• 7 teams okay...for a match u need 2 teams.suppose there r totally 'n 'teams.Now you have to choose 2 teams out of 'n' teams.so answer =no of such choices=no. of possible combinations. So we've ans = nC2(ncombination2)=21;solve to get n=7.
  Sol : n(n-1)/2=21. so n=7.if u don't understand c the graph below each team plays no. of matches = no of teams ahead of it. One bar represents one team. ------------7 6 5 4 3 2 1 0 -----------21 last team is written as 0 matches because this team has already played with all other teams-hence sum of matches =6+5+4+3+2+1=21 which is correct only if no of teams =7 :)
• 11 years agoHelpfull: Yes(5) No(1)