CAT 2007 — QA Question 11
Permutation & CombinationEasy
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?
Answer & solution
Correct answer: n(k – 1)
n(k – 1)
- B
k(n – 1)
- C
n(k – 2)
- D
k(k – 2)
- E
(n – 1)(k – 1)
Solution
Each team has (k – 2) players to itself and shares 2 players with other two teams.
n pairs of teams have 1 player in common and there are n teams.
Total number of players = n(k – 2) + n
= nk – 2n + n
= nk – n
= n(k – 1)
Hence, option (a).