Question

In the next World Cup of cricket there will be 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 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. None of these

Answer 1

Answer: (B)

53

Answer 2

The number of matches in the first round = ⁶C₂ + ⁶C₂

The number of matches in the next round = ⁶C₂.

The number of matches in the semifinal round = ⁴C₂

\ the required number of matches

= ⁶C₂ + ⁶C₂ + ⁶C₂ + ⁴C₂ + 2.