Combination in competition
16 teams enter a competition. They are divided up into four Pools(A, B, C and D) of four teams each.
Every team plays one match against the other teams in its Pool.
After the Pool matches are completed: • the winner of Pool A plays the second placed team of Pool B • the winner of Pool B plays the second placed team of Pool A • the winner of Pool C plays the second placed team of Pool D • the winner of Pool D plays the second placed team of Pool C
The winners of these four matches then play semi-finals, and the winners of the semi-finals play in the final.
How many matches are played altogether?
For more problems ,click here .
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
The number of matches played in each Pool is "4 choose 2" = 4C2 = 4!/(2!2!) = (4 × 3)/(2 × 1) = 6
Why "4 choose 2"? Because you are choosing 2 teams to play each other out of 4 (in the pool). Order does not matter (A plays B is the same as B plays A).
Imagine 4 teams (A,B,C,D):
A plays B
A plays C
A plays D
B plays C
B plays D
C plays D
They each get to play each other, 6 games in total
With 4 pools, the total number of Pool matches = 4 × 6 = 24
The winners and second placed teams play a further 4 matches. Then there are 2 semi-finals and 1 final
So the total number of matches = 24 + 4 + 2 + 1 = 31