In a tournament there are n teams T1 T2 hellip hellip Tn with n gt 5 Each team consists of k player...........

Quantitative Aptitiude (CLAT) Number System

In a tournament, there are n teams T₁, T_2, ……. 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 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?

k (n – 1)

n(k – 2)

k (n – 2)

n (k - 1)

Explanation:

Total no.of teams=n
each team has k players.
on folllwing the given data,
let n=6&k=4
req no of players=18(1 common in each 6 teams)
T1&T2= 1 common player
T2&T3=1 common player
T3&T4=1 common player
T4&T5=1 common player
T5&T6=1 common player
T6&T1=1 common player
a)k(n-1)=4(6-1)=20
b)n(k-2)=6(4-2)=12
c)k(n-2)=4(6-2)=16
d)n(k-1)=6(4-1)=18