Question 1157980: An organization has 120 members
How many possible ways can we partition the members of this organization into 10 committees with 12 members each?
Answer by KMST(5376)   (Show Source):
You can put this solution on YOUR website! I believe the answer expected would be 
If you start by picking a group of 12 people for one of the committees, you have  ways to make a list,
but there could be other lists with the same names in different orders, for a total of
 such lists,
So there are  ways to pick the first group of 12 from the 120 organization members.
You could then pick from the 108 remaining members a second group of 12 in
 ways,
then you could pick from the 96 remaining members a group of 12 in
ways,
then you could pick from the 96 remaining members a group of 12 in
 ways,
then you could pick from the 84 remaining members a group of 12 in
 ways,
And so on until you have used all 120 members of the organization and you have a list with
 lists of 10 groups in the order picked.
If the first entry in your is
(group A, group B, group C, group D, group E, group F, group G, group H, group I, group J) picked in that order,
the same set of groups appears in  different orders down your list. Each set of 10 groups appears times, just with the group listed in different orders,
and nowhere it says that the order the committees were chosen matters, so we have to divide by .
|
|
|
