In a tournament, there are n teams T1 , T2 ....., Tn with n > 5. Each team consists of k players, k > 3. The following pairs of teams have one player in common: T1 & T2 , T2 & T3 ,......, Tn − 1 & Tn , and Tn & 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?  Choose the most appropriate option:  A) n(k-1)  B) k(n-1)  C) n(k-2)  D) k(n-2)  E) (n-1)(k-1)
Explanation :   Let T1 - T6 be the number of teams, and let 1,2,3,4,5,6….be the players in the teams.   Total players if there are no repetition is 6*4 here. Generally, it is n * k. (n = number of teams, k = player/team). However, we see that, in each team, 1 player is repeated. i.e.   T1 &amp; T2 have 4 in common (So 1 can be subtracted)   T2 &amp; T3 have 7 in common (So 1 can be subtracted)   T3 &amp; T4 have 10 in common (So 1 can be subtracted)   T4 &amp; T5 have 13 in common (So 1 can be subtracted)   T5 &amp; T6 have 16 in common (So 1 can be subtracted)   T6 &amp; T1 have 1 in common (So 1 can be subtracted)   So, totally from each column 1 can be subtracted.   There are “n” columns totally, so n can be subtracted ( Here 6 needs to be subtracted)   So, here we have 6 * 4 – 6 players. Generally we have n * k – n i.e n(k-1) players.   n(k-1)nswer : n(k-1)
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In a tournament, there are n teams T1 , T2 ....., Tn with n > 5. Each team consists of k players, k > 3. The following pairs of teams have one player in common: T1 & T2 , T2 & T3 ,......, Tn − 1 & Tn , and Tn & 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?