Question

In a football competition, there are 4 teams. Each team plays each other once. What is the total number of matches played?

a) 6
b) 12
c) 3
d) 2
e) 4
f) 16
g) 15

Answer 1

The total number of matches played in the football competition is 6. Hence, a) is correct.

Step-by-step explanation:

There are 4 teams in the football competition. Each team plays each other once. To find the total number of matches played, we can use the combination formula. Since each team plays every other team once, we can choose 2 teams from the 4 teams. The formula for finding the number of combinations is:

nCr = n! / (r!(n-r)!)

Plugging in the values, we get:

nCr = 4! / (2!(4-2)!)

= 4! / (2!2!)

= (4 x 3 x 2 x 1) / ((2 x 1)(2 x 1))

= 24 / (2 x 2)

= 24 / 4

= 6

Therefore, the total number of matches played in the competition is 6.