in how many ways can 9 students be exactly divided into 3 teams

Question

amistre64 · Answer

im thinking 9 choose 3, but that prolly wrong, any ideas?

here_to_help15 · Answer

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amistre64 · Answer

3 people teams in not picking whos on a team tho

here_to_help15 · Answer

Oh wait wait i read it wrong..

amistre64 · Answer

there are 9 choose 3 ways to create 1 team, right?

amistre64 · Answer

and all those choices make up all the possible teams that can be made

here_to_help15 · Answer

So @tanjung split 9 into 3 to exactly fit 3 teams.

anonymous · Answer

so, can one of a tim has one member ? 2 members ? 3 members ? and so on

here_to_help15 · Answer

3 people per team is the only way it can fit exactly

here_to_help15 · Answer

So given that 9 divded by 3 equals 3 teams only so i believe there is only 3 ways ? @amistre64 now i am starting to get mixed up 0.O

amistre64 · Answer

i can prove that there are more than 3 ways just by listing at least 4 ways right?

amistre64 · Answer

abc   def   ghi

abd   cef   ghi

abd   gef   chi

gbd   aef   chi

here_to_help15 · Answer

Woah

here_to_help15 · Answer

blew me away o.O thanks for the (  ^      (back up)

here_to_help15 · Answer

< ^

anonymous · Answer

number member of each team must be same ? @amistre64

amistre64 · Answer

to choose 3 people for a team out of 9

there 9C3 teams,  9*8*7  sets of unique teams

and we want to group 3 of them together,  (9*8*7) C 3 ways o do that

amistre64 · Answer

i might have to chk to make sure ive got my P or C correctly

here_to_help15 · Answer

Oops i meant to delete that o.o

amistre64 · Answer

9C3 = 84

84C3 = about 95k or a little more

amistre64 · Answer

id hate to have to write them all out if thats the case

amistre64 · Answer

9C3 ways to pick the first team

6C3 ways to pick the next team

3C3 ways to pick the last team

... now im getting 105, which i think is the most sensible result

anonymous · Answer

is it correct :
for the first team = 9C3 = 84
for the 2nd team = 6C3 = 20
for the last team = 3C3 = 1
totaly = 84 x 20 x 1 = 1680 ?

amistre64 · Answer

ive thought of 3 different ways to try to think about it and all of them come up different answers,  but yes  1680 seems fair to me,  i added instead of multiplied and got the 105 :)

anonymous · Answer

so, the correct answer is 1680 ?

amistre64 · Answer

im not confident to say its the correct answer, but it does make the most sense to me.

here_to_help15 · Answer

http://gmatclub.com/forum/in-how-many-different-ways-can-a-group-of-9-people-be-divide-101722.html

here_to_help15 · Answer

i tried screen shotting the formula but the thing wouldn't let me.