112 There are m teams in league A and n teams in league B On

1.12. There are m teams in league A and n teams in league B. On game day there are k games played (k n and k m); each game pits a team from league A against a team from league B. A given team can play at most once on game day. How many different sets of match-ups (^\'\'schedules^\'\') can be made for game day? (a) If a ^\'\'schedule^\'\' includes the teams playing and a distinct time for each of the k games? (b) If a ^\'\'schedule^\'\' includes only the team match-ups and no information on time?

Solution

a)

We can choose P(n, k) = n! / (n - k)! ways for teams in league A.

Then we chose permutations for the teams in leage B to make different matchups: P(m, k) = m! / (m - k)!.

Thus, multiplying these, there are

#schedules = [n! m!] / [(n - k)! (m - k)!] [ANSWER]

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b)

Now, if order of matches do not matter, then we can divide the schedule by k! ways to permute the matches. Thus,

#schedules = [n! m!] / [k! (n - k)! (m - k)!] [ANSWER]