Group Stage of FIFA World Cup 2018

Probability Level 1

How many matches were played in the group stage of FIFA World Cup 2018?

Important information:

  1. A total of 32 teams played in the group stage.
  2. The teams were divided into 8 groups.
  3. A team played once against each of the other teams of its group.

Image credits: Wikipedia

32 46 40 36 56 48 50

Muhammad Arifur Rahman by Muhammad Arifur Rahman , 23, Bangladesh

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5 solutions

Brian Moehring
Jul 7, 2018

Each group has 32 8 = 4 \frac{32}{8} = 4 teams and in a group of four, there are ( 4 2 ) = 6 \binom{4}{2} = 6 ways to choose two teams to play a match.

Therefore # matches = ( # groups ) ( # matches per group ) = 8 ⋅ 6 = 48 \#\text{matches} = \left(\#\text{groups}\right)\left(\#\text{matches per group}\right) = 8 \cdot 6 = \boxed{48}

11 Helpful 0 Interesting 0 Brilliant 0 Confused

@Brian Moehring That's a straightforward solution 👌

Muhammad Arifur Rahman - 2 years, 11 months ago
Noel Lo
Jul 11, 2018

Each group has 32 8 = 4 \dfrac{32}{8}=4 teams where ( 4 2 ) = 6 \dbinom {4}{2}=6 games are played, giving us a total of 8 × 6 = 48 8\times 6=\boxed{48} games.

5 Helpful 0 Interesting 0 Brilliant 0 Confused
Szsmix Seb
Jul 23, 2018

There are 32 teams. All of them will play 3 matches in the group stage. 32÷2 = 16 matches played when all the teams played once. 16×3 = 48.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Firts Last
Jul 9, 2018

GOOGLE IT.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Why didn't I think of that? lmao

Sören Fischötter - 2 years, 11 months ago

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Because you tried to learn, which is very nice 👍

Muhammad Arifur Rahman - 2 years, 11 months ago

That's more straightforward solution, but probably not "learning-friendly" 😛

Muhammad Arifur Rahman - 2 years, 11 months ago
J'Neal Caldwell
Jul 15, 2018

I solved it this way. 32/8 equal 4, fo there are 4 in each group. To solve for the combinations in each group, I used a factorial of 3 ([4-1]!) to get 6, the total number of games in each group of 4, and multiplied that by 8 to get 48 as the total number of games.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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