SOLUTION: 30 kids, gold silver and bronze medals, how many different winning arrangements can there be if each team consists of 5 students?

Question 163939: 30 kids, gold silver and bronze medals, how many different winning arrangements can there be if each team consists of 5 students?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
I'll take a stab at it
Here's 6 teams, 5 students each:
team 1: a b c d e
team 2: a b c d e
team 3: a b c d e
team 4: a b c d e
team 5: a b c d e
team 6: a b c d e
Assume 1a gets the gold. How many ways can the other teams
get the Silver?
There are 25 students in the remaining 5 teams, so there are
25 ways the Silver can be given
If 1b gets the Gold, also 25 ways to give Silver, etc
So, if someone from team 1 gets Gold, there are
ways to give Silver
If someone from team 2 gets Gold, also ways
So, for all 6 teams:
ways to give Silver
Now 1 team has Gold and 1 team has Silver
There are 20 students in the remaining 4 teams
For each of the combinations of Gold and Silver,
there are 20 ways to give Bronze.

There are 15000 different winning arrangements
This seems pretty large. Check my reasoning-maybe it's off

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