Total participants in tournament teams

CAT 2007 Slot 1 · QA · Medium · Combinatorics

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In a tournament, there are nn teams T1,T2,…,TnT_1, T_2, \dots, T_n, with n>5n > 5. Each team consists of 'kk' players, k>3k > 3. The following pairs of teams have one player in common: T1&T2,T2&T3,…,Tn−1&TnT_1 \& T_2, T_2 \& T_3, \dots, T_{n-1} \& T_n, and Tn&T1T_n \& T_1. No other pair of teams has any player in common. How many players are participating in the tournament, considering all the 'nn' teams together?

  1. A.

    n(k−1)n(k - 1)

  2. B.

    k(n−1)k(n - 1)

  3. C.

    n(k−2)n(k - 2)

  4. D.

    k(n−2)k(n - 2)

  5. E.

    (n−1)(k−1)(n - 1)(k - 1)

Answer

A

Explanation

Each team has kk players. There are nn shared players between adjacent teams. Each of these nn shared players belongs to 2 teams. Total unique players =n×(k−2)+n=n(k−1)= n \times (k - 2) + n = n(k - 1).

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