## ezhyl_marie one year ago 16 teams enter a competition. They are divided up into four pools(A, B, C,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?

1. ezhyl_marie

help me ..

2. ezhyl_marie

it is a probability question. What formula did you used ?

3. Yttrium

Let's consider the first case. for every pool there are 4 groups right? I think we can use here the 4P4 = 24

4. ezhyl_marie

hm. then ?

5. ***[ISURU]***

the number of way that a set of n can be arrange is given by n!

6. ***[ISURU]***

The number of matches played in each Pool = (4 × 3)/(2 × 1) = 6 So 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

7. Yttrium

then there are four battles for the case 2 (after pool matches are comleted) = 4 then case 3 (winners of case 2 to fight for semi-finals) = 2 case 4 (battle for finals) = 1 Hence it is 24+4+2+1 = 31