Scheduling Combinatorics Quiz

Other Math and Science
1

*40 teams show up for an imaginary FRC competition.

Ignoring alliance colors, all possible matches are played.

Questions:

  1. How many matches are played?

  2. How many matches does any given team play?

  3. How many times do any 2 given teams play WITH each other?

  4. How many times do any 2 given teams play AGAINST each other?

2

3 teams per alliance?
2 alliances per match?

3

Yes. FRC.

4

Lazy Approach
[spoiler]
(40 Choose 3)(37 Choose 3)/2
(39 Choose 2)(37 Choose 3)
(38 Choose 1)(37 Choose 3)
(38 Choose 2)(36 Choose 2)
[/spoiler]

5

Nicely done !

1, 3, & 4 could also be calculated using:

  1. [sub]40[/sub]C[sub]6[/sub]*[sub]6[/sub]C[sub]3[/sub]/2

  2. same as yours

  3. (ans#2)(2)/39

  4. (ans#2)(3)/39