In the local frisbee league, teams have 7 members and each of the 4 teams takes turns hosting tournaments. At each tournament, each team selects two members of that team to be on the tournament committee, except the host team, which selects three members. How many possible 9 member tournament committees are there?


Any help is greatly appreciated 

 Jul 21, 2018

Here is my 'stab' at it    (BE WARNED:I often get these answers incorrect)

4   ways to pick the host team          4

EACH of remaining 3 teams have 7c2 ways to pick committee members     7c2 * 7c2 * 7c2

and the host team has 7c3 ways to pick committee members       7c3

4*  7c2 * 7c2 * 7c2 * 7c3 = 4 x 21 x 21 x 21 x 35 = 1296540 ways


(I hope I got this one!)

 Jul 21, 2018

I don’t get how you approached the problem. Please elaborate on the answer just a bit more

 Jul 22, 2018

Thank you though, because the answer is correct

 Jul 22, 2018

7c2  is how many different combinations of 2 you can make out of 7 choices


For EACH of those combinations the second team can make 7c2 choices

    and for EACH of THOSE choices the THIRD team can make  7c2 choices

      and for EACH of THOSE choices, the FOURTH team can make 7 c 3 choices


7c2 = 21     7c3 = 35


THEN there are FOUR ways to pick the host team , multiply THAT by 4:


7c2  x  7c2   x 7c2  x  7c3  x 4

 Jul 22, 2018

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