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

Explanation

To solve the problem of calculating the minimum number of matches in the next World Cup of cricket, we will break it down step by step.

### Step 1: Group Division and Initial Matches
There are 12 teams divided into 2 groups of 6 teams each. In each group, every team plays against every other team.

- **Number of matches in one group**: The number of matches played among 6 teams can be calculated using the combination formula \( C(n, 2) \), where \( n \) is the number of teams.

\[ \text{Matches in one group} = C(6, 2) = \frac{6!}{2!(6-2)!} = \frac{6 \times 5}{2 \times 1} = 15 \]

- **Total matches for both groups**:

\[ \text{Total matches} = 15 + 15 = 30 \]

### Step 2: Qualification for Next Round
From each group, the top 3 teams qualify for the next round. Therefore, there are 6 teams in total in the next round.

### Step 3: Matches in the Next Round
In this round, each of the 6 teams plays against every other team once.

- **Number of matches in the next round**:

\[ \text{Matches in next round} = C(6, 2) = \frac{6!}{2!(6-2)!} = \frac{6 \times 5}{2 \times 1} = 15 \]

### Step 4: Semi-Final Matches
From the next round, the top 2 teams will qualify for the final. The number of matches played among the 4 top teams (the top 3 from the previous round) can be calculated as:

- **Number of matches among 4 teams**:

\[ \text{Matches among 4 teams} = C(4, 2) = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2 \times 1} = 6 \]

### Step 5: Final Matches
In the final round, the top 2 teams will play a best of 3 matches. The minimum number of matches required can be 2 if one team wins the first two matches.

### Step 6: Total Matches Calculation
Now, we can sum up all the matches calculated:

- Matches from group stage: 30
- Matches from the next round: 15
- Matches from semi-finals: 6
- Matches from finals: 2 (minimum)

\[ \text{Total matches} = 30 + 15 + 6 + 2 = 53 \]

Thus, the minimum number of matches in the next World Cup will be **53**.