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In a tournament, there are n teams, T1, T2, T3 ...., Tn, with n > 5. Each team consists of K players K > 3. - Mathematics

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MCQ

In a tournament, there are n teams, T1, T2, T3 ...., Tn, 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,..., Tn-1 and Tn and Tn 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)

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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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