Question

Twenty four teams are divided into 4 groups of six teams each. Within each group the teams play each other exactly once. The winners of each group then play in the semi-finals. Winners of the semi-finals play in the finals and losers for the 3rd place. How many matches are played?

• A. $60$
• B. $63$
• C. $64$
• D. $66$

Answer 1

Answer: (C)

$64$

4 groups of 6 teams each.
In a group there will be ${}^6{P}_2$ matches
$\frac{6!}{(6-2)}=\frac{6\times 5}{2}=15$
This can also be calculated in other way $=5+4+3+2+1=15$ matches
[Team1 plays 5 matches with others.
Team 2 plays 4 matches with remaining others.
Team 3 plays 3 matches with remaining others.. Team 4 plays 2 matches with remaining others.
Team 5 plays 1 matches with remaining others.
Only Team 6 remains who has played will all above teams.]
So Total matches in Round $1=15\times 4=60$
Semifinals $=2$
Final & 3rd position play off $=2$
Thus $60+2+2=64$ in all.
Hence, option 'C' is correct.