MCQ

In a tournament, there are n teams, T_{1}, T_{2}, T_{3} ...., T_{n}, with n > 5. Each team consists of K players K > 3. The following pairs of teams have one player in common T_{1} and T_{2}, T_{2} and T_{3},..., T_{n-1} and T_{n} and T_{n} and T_{1}. No other pair of teams has any player in common. How many players are participating in the tournament, considering all the n teams together?

#### Options

K (n -1)

n (K -2)

K (n -2)

n(K –1)

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#### Solution

**n (K -2)**

**Explanation:**

Number of teams = n(n > 5)

Number of player in 1 team = K(K > 3)

Now, consider team 1

It has number of player = k (k > 3)

Now, number of player common with the other team (Tn ,T2) = 2

So, number of uncommon player in each team = K –2 and number of teams = n

∴ Total number of players = n (K–2)

Concept: Ratio and Proportion (Entrance Exam)

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