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:-
![^nC_r=\dfrac{n!}{r!(n-r)!}](https://tex.z-dn.net/?f=%5EnC_r%3D%5Cdfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D)
Similarly, the number of combination to arrange 7 teams if 2 teams are taken at a time:-
![^7C_2=\dfrac{7!}{2!(7-2)!}\\\\=\dfrac{7\times6\times5!}{2\times5!}=21](https://tex.z-dn.net/?f=%5E7C_2%3D%5Cdfrac%7B7%21%7D%7B2%21%287-2%29%21%7D%5C%5C%5C%5C%3D%5Cdfrac%7B7%5Ctimes6%5Ctimes5%21%7D%7B2%5Ctimes5%21%7D%3D21)
∴ 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: ![21\times2=42](https://tex.z-dn.net/?f=21%5Ctimes2%3D42)
Hence, There will be 42 games played.