Answered

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There are 18 football teams in a league,
Each team plays two matches against each of the other teams,
Work out the total number of matches played,

Sagot :

rhyscain

Answer:

306

Step-by-step explanation:

18x17=306

The total number of matches played by the teams will be given by using permutation is 306.

What are permutation and combination?

A permutation is an act of arranging the objects or elements in order. Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.

There are 18 football teams in a league.

Each team plays two matches against each of the other teams.

Then the total number of matches played by the teams will be given by the permutation.

[tex]^{n}P_r = \dfrac{n!}{(n-r)!}[/tex]

We have

n = 18

r = 2

Then

[tex]\rm ^{18}P_2 = \dfrac{18!}{(18-2)!}\\\\\\^{18}P_2 = \dfrac{18!}{16!}\\\\\\^{18}P_2 = \dfrac{18 *17*16!}{16!}\\\\\\^{18}P_2 = 18*17\\\\\\^{18}P_2 = 306[/tex]

More about the permutation and the combination link is given below.

https://brainly.com/question/11732255

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