(a)[4]
Determine the number of distinct ways to choose the team of $7$ if it contains exactly $1$ swimmer, at least $4$ cyclists and at most $2$ runners.
(b)[2]
In a different competition, a team of $9$ people includes $2$ swimmers, $3$ cyclists and $4$ runners. The team members line up for a photograph. How many distinct line-ups are possible for the $9$ people if the swimmers stay together, the cyclists stay together and the runners stay together?
(c)[4]
How many distinct line-ups are there of the $9$ people if no two cyclists are adjacent?