Answer: There will be 42 games played.
Step-by-step explanation:
The number of combination to arrange n things if r things are taken at a time:-
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Similarly, the number of combination to arrange 7 teams if 2 teams are taken at a time:-
[tex]^7C_2=\dfrac{7!}{2!(7-2)!}\\\\=\dfrac{7\times6\times5!}{2\times5!}=21[/tex]
∴ Number of combination to arrange 7 teams if 2 teams are taken at a time=21
Also, each team plays each of the other teams twice.
Then, the number of games will be played: [tex]21\times2=42[/tex]
Hence, There will be 42 games played.
