document.write( "Question 163939: 30 kids, gold silver and bronze medals, how many different winning arrangements can there be if each team consists of 5 students? \n" ); document.write( "

Algebra.Com's Answer #120804 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'll take a stab at it
\n" ); document.write( "Here's 6 teams, 5 students each:
\n" ); document.write( "team 1: a b c d e
\n" ); document.write( "team 2: a b c d e
\n" ); document.write( "team 3: a b c d e
\n" ); document.write( "team 4: a b c d e
\n" ); document.write( "team 5: a b c d e
\n" ); document.write( "team 6: a b c d e
\n" ); document.write( "Assume 1a gets the gold. How many ways can the other teams
\n" ); document.write( "get the Silver?
\n" ); document.write( "There are 25 students in the remaining 5 teams, so there are
\n" ); document.write( "25 ways the Silver can be given
\n" ); document.write( "If 1b gets the Gold, also 25 ways to give Silver, etc
\n" ); document.write( "So, if someone from team 1 gets Gold, there are
\n" ); document.write( " $\"5%2A25+=+125\"$ ways to give Silver
\n" ); document.write( "If someone from team 2 gets Gold, also $\"125\"$ ways
\n" ); document.write( "So, for all 6 teams:
\n" ); document.write( " $\"6%2A125+=+750\"$ ways to give Silver
\n" ); document.write( "Now 1 team has Gold and 1 team has Silver
\n" ); document.write( "There are 20 students in the remaining 4 teams
\n" ); document.write( "For each of the $\"750\"$ combinations of Gold and Silver,
\n" ); document.write( "there are 20 ways to give Bronze.
\n" ); document.write( " $\"750%2A20+=+15000\"$
\n" ); document.write( "There are 15000 different winning arrangements
\n" ); document.write( "This seems pretty large. Check my reasoning-maybe it's off\r
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