Question

In the next world cup of cricket, there will be $12$ teams, divided equally into 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 other once. Four top teams from this round, where each team will play against the other three. Two top teams of this round will goto the final round, where they will play the best of three matches. The minimum number of matches in the next world cup will be

• A. $54$
• B. $53$
• C. $38$
• D. $55$

Answer 1

Answer: (B)

$53$

No. of matches in first round ${=}^6{C}_2{+}^6{C}_2$
No. of matches in next round ${=}^6{C}_2$
No. of matches in Semifinal round ${=}^4{C}_2$
So required number of matches ${}^6{C}_2{+}^6{C}_2{+}^6{C}_2{+}^4{C}_2+2=53$ (minimum $2$ matches must be played in best of $3$)