Ten teams participate in a tournament. Every team plays each of the other teams twice. The total number of matches to be played is: A. 20 B. 45 C. 60 D. 90

GATE 2012 · General Aptitude · Combinatorics · medium

Answer: 90 matches (option D)

1. Count unique team pairs: C(10,2) = 10!/(2!*8!) = (10*9)/2 = 45.
2. Multiply for double round-robin: Each pair plays twice: total matches = 45 x 2 = 90.