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 other once. Each of the four top teams of this round will play amatch against the other three. Two top teams of this round will go to the final round, where they will playthe best of three matches. The minimum number of matches in the next world cup will be

Options

A. 54
B. 53
C. 38
D. 37

Answer

B

Explanation

The number of mathces in the first round`=.^(6)C_(2)+.^(6)C_(2)=30`
The number of matches in the next round`=.^(6)C_(2)=25`
and the number of matches in the semi-final round`=.^(4)C_(2)=6`
`therefore`The required number of matches=30+15+6+2=53
[`because` for 'best of three' atleast two matches are played].