document.write( "Question 1157980: An organization has 120 members\r
\n" ); document.write( "\n" ); document.write( "How many possible ways can we partition the members of this organization into 10 committees with 12 members each? \n" ); document.write( "
Algebra.Com's Answer #854511 by KMST(5377)\"\" \"About 
You can put this solution on YOUR website!
I believe the answer expected would be \"120%21%2F12%21%5E2%2F10%21\"
\n" ); document.write( "If you start by picking a group of 12 people for one of the committees, you have \"120%2A119%2A118%2A%22...%22%2A110%2A109\" ways to make a list,
\n" ); document.write( "but there could be other lists with the same names in different orders, for a total of
\n" ); document.write( "\"12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2=12%21\" such lists,
\n" ); document.write( "So there are \"120%2A119%2A118%2A%22...%22%2A110%2A109%2F12%21\" ways to pick the first group of 12 from the 120 organization members.
\n" ); document.write( "You could then pick from the 108 remaining members a second group of 12 in
\n" ); document.write( "\"108%2A107%2A106%2A%22...%22%2A98%2A97%2F12%21\" ways,
\n" ); document.write( "then you could pick from the 96 remaining members a group of 12 in
\n" ); document.write( "\"108%2A107%2A106%2A%22...%22%2A98%2A97%2F12%21\" ways,
\n" ); document.write( "then you could pick from the 96 remaining members a group of 12 in
\n" ); document.write( "\"96%2A95%2A94%2A%22...%22%2A86%2A85%2F12%21\" ways,
\n" ); document.write( "then you could pick from the 84 remaining members a group of 12 in
\n" ); document.write( "\"84%2A83%2A82%2A%22...%22%2A74%2A73%2F12%21\" ways,
\n" ); document.write( "And so on until you have used all 120 members of the organization and you have a list with
\n" ); document.write( "\"120%21%2F12%21%5E2\" lists of 10 groups in the order picked.
\n" ); document.write( "If the first entry in your is
\n" ); document.write( "(group A, group B, group C, group D, group E, group F, group G, group H, group I, group J) picked in that order,
\n" ); document.write( "the same set of groups appears in \"10%21\" different orders down your list. Each set of 10 groups appears \"10%21\" times, just with the group listed in different orders,
\n" ); document.write( "and nowhere it says that the order the committees were chosen matters, so we have to divide \"120%21%2F12%21%5E2\" by \"10%21\" .\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );