Question

Twenty four teams are divided into $4$ groups of six teams each. Within each group the team 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 $3$ place. How many matches are played?

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

Answer 1

The correct option is B $63$

There are $24$ teams divided into $4$ groups of six teams each.

As in each group the teams play with each other exactly once, so the number of matches played for one group will be ${}^6{C}_4$.

${}^6{C}_4=\frac{6!}{4!2!}=15$.

Since there are 4 groups, so total no. of matches played by $4$ groups $=15\times 4=60$.

Now the winners will play in semi-final.

To decide the finalist, two-two teams play the match.

So, the no. of matches played in semifinal is $2$.

And $1$ match will be played in the final.

So, total no. of matches played $=60+2+1=63$.

Hence, option B is correct.