Question

In a tournament, there are n teams, T₁, T₂, T₃ ...., T_n, with n > 5. Each team consists of K players K > 3. The following pairs of teams have one player in common T₁ and T₂, T₂ and T₃,..., T_n-1 and T_n and T_n and T₁. 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)

Answer 1

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)