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

Memes4Life132 Jul 21, 2018

#1**0 **

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!)

ElectricPavlov Jul 21, 2018

#2**0 **

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

Memes4Life132 Jul 22, 2018

#4**0 **

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

ElectricPavlov Jul 22, 2018