Question

In world cup of cricket there are $12$ teams ,divided equally in two groups. Teams of each group will play a match against each other. From each group $3$ top teams will qualify for the next round. In this round each team will play against others once. Four top teams of this round will qualify for the semifinal round, where each team will play against the others once. Two top teams of this round will go to final round, where they will play the best of three matches. The minimum number of matches in the World Cup will be

• A. $54$
• B. $53$
• C. $38$
• D. $40$

Answer 1

Answer: (B)

$53$

Answer 2

The number of matches in the first round $=\,^{6}C_{2}+\,^{6}C_{2}=15+15=30$ The number of matches in the next round $=\,^{6}C_{2}=15$ The number of matches in the semi-final round $=\,^{4}C_{2}=6$ $\therefore$ the reqd. number of matches $=30+15+6+2=53$ ($\because$ for best of three at least two matches are played)