Question

Word Problem please help!

There are 30 teams in major league baseball. If each team played each other team exactly 5 times, what would be the total number of games played?

Answer 1

\(\Large hint:\qquad nCr\)

Answer 2

ok i have to show work, whats a good way to start?

Answer 3

Team 1 plays the other 29 teams 5 times each: 5 x 29.
Because Team 1 and 2 have already played 5 times (see sentence above),
Team 2 only needs to play 28 teams 5 times each: 5 x 28.
Because Team 1 and 3 have already played 5 times (see sentence 1 above) and
Team 2 and 3 have already played 5 times (see sentence 2 above),
Team 3 only needs to play 27 teams 5 times each: 5 x 27.
This pattern continues, so you have 5x29 + 5x28 + 5x27 + ... + 5x1 = 5(29+28+27+...+1)

Answer 4

@Stacey, this makes so much sense!