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.

Explanation:

The number of combination to arrange n things if r things are taken at a time:-

`^nC_r=(n!)/(r!(n-r)!)`

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

`^7C_2=(7!)/(2!(7-2)!)\\\\=(7*6*5!)/(2*5!)=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*2=42`

Hence, There will be 42 games played.