Question

For a chess tournament $13$ people were selected for quarter finals. Each person plays two matches with the other. How many matches have been held in the whole tournament?

• A. $144$
• B. $156$
• C. $185$
• D. $116$

Answer 1

The correct option is B $156$

$13$ People Each people plays two matches

Selecting two players and letting them play

$={}^{13}{P}_2$

$=\frac{13\times 12\times 11\times 10\times .......3\times 2\times 1}{11!}$

$=13\times 12$

$=156$

Hence Number of matches is $156$