Question

14 of 16 (12 complete) In a baseball league consisting of 7 teams, each team plays each of the other teams twice. How many games will be played? There will be games played.

Answer 1

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:-

$^nC_r=\dfrac{n!}{r!(n-r)!}$

Similarly, the number of combination to arrange 7 teams if 2 teams are taken at a time:-

$^7C_2=\dfrac{7!}{2!(7-2)!}\\\\=\dfrac{7\times6\times5!}{2\times5!}=21$

∴ 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: $21\times2=42$

Hence, There will be 42 games played.