There are fourteen teams playing in a tournament. If every team plays one match with every other team, how many matches will be played in the tournament?
एक प्रतियोगिता में चौदह टीमें खेल रही हैं | यदि प्रत्येक टीम हर दूसरी टीम से एक मैच खेलती है, तो इस प्रतियोगिता में कुल कितने मैच खेले जायेंगे?

Options

A. 105
B. 91
C. 85
D. 78

Answer

B

Explanation

Total number of teams = 14.
Required number of matches played
`= ""^(14)C_2 = (14!)/(2!(14 - 2)!) = (14!)/(2! 12!)`
`= (14 xx 13 xx 12!)/(2 xx 1 xx 12!) = 91`
[Note : Formula : `""^nC_r = (n!)/(r!(n - r)!)]`