There are 16 hockey teams. find :
(1) Number of matches played when each team plays with each other twice.
(2) Number of matches played when each team plays each other once.
(3) Number of matches when knockout of 16 team is to be played
(1)260 (2)140 (3)15
(1)220 (2)180 (3)25
(1)280 (2)220 (3)35
(1)240 (2)120 (3)15
Explanation:
1. Number of ways that each team played once with other team = 16C216C2. To play with each team twice = 16 x 15 = 240
2. 16C216C2 = 120
3. Total 4 rounds will be played. Total number of matches required = 8 + 4 + 2 + 1 = 15