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?
Choose the correct answer:
A) 6 teams	B) 7 teams	C) 5 teams	D) 4 teams	E) 2 teams
For a match you need 2 teams.suppose there are 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 ———–21last 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= 
<gadget id="calculator">6+5+4+3+2+1</gadget>
<output>21</output>
21 which is correct only if no of teams=7   answer is :7 teams   Answer 7 teams
<result>B</result>
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?