Question

There are 16 different teams in a football league. Two teams are going to be chosen at random to play a match. Work out the number of different matches that could take place.

A) 16 ways
B) 120 ways
C) 136 ways
D) 256 ways

Answer 1

The number of different matches that could take place between 16 teams is calculated using the combination formula, giving a total of 120 different ways.

Step-by-step explanation:

To work out the number of different matches that could take place between 16 different teams, where two teams are chosen at random to play each other, we can use the formula for combinations, which is:

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

• n is the total number of items,
• r is the number of items to choose.

Here, n is 16 (the number of teams) and r is 2 (the number of teams we want to play a match). Therefore:

16C2 = 16! / (2!(16-2)!) = 16! / (2!14!) = (16 x 15) / (2 x 1) = 240 / 2 = 120

There are 120 different ways for the matches to take place, which corresponds to option B.