In a tournament 14 teams play league matches. If each team plays against every other team once only then how many matches are played? [UPSC 2010 (CS-P)]
a) 105
b) 91
c) 85
d) 78

• 1 team play 13 matches
  Its means total matches = 13×14 ÷2=91
• 9 years agoHelpfull: Yes(1) No(0)
• It is similliar like hand shanking problem think theory of permutation and combination 14C2=(14*13)/2=91
• 8 years agoHelpfull: Yes(1) No(0)
• 91
  You have 14 teams- a,b,c,d,f,g,h,j,k,l,m,n,p,q
  a plays b,c,d,f,g,h,j,k,l,m,n,p,q= 13 matches
  b plays c,d,f,g,h,j,k,l,m,n,p,q= 12
  c plays d,f,g,h,j,k,l,m,n,p,q=11
  and so on through the line up
  you get 13+12+11+10+9+8+7+6+5+4+3+2+1
  for a total of 13! matches, or 91 matches.
  
• 10 years agoHelpfull: Yes(0) No(0)
• 91 matches
• 10 years agoHelpfull: Yes(0) No(0)