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!)