NZ Olympics Committee sent a delegation of 212 competitors to the Tokyo Olympics 2020/21. In particular, they sent 13 co

[answerhappygod]

NZ Olympics Committee sent a delegation of 212 competitors to
the Tokyo Olympics 2020/21.
In particular, they sent 13 competitors for athletics, 8 for
canoeing, 2 for shooting, 10 for sailing
and 19 for cycling.
Give proper reasoning and answer the following. You won’t get full
marks if you just write
down the answer without justifying.
(a) In how many ways can you form a 10 member group that consists
of 3 competitors from
athletics, 2 from sailing, 2 from shooting, 2 from canoeing and 1
from cycling?
(b) In how many ways can you form a 5 member group (from the entire
delegation of 212)
that contains at least 3 competitors from canoeing, and no
competitors from cycling,
athletics or sailing?
(c) The 20 competitors from canoeing, shooting and sailing decide
to take a group photo.
The photographer gives them the following instructions. They must
sit in two rows of 10.
The 2 shooting competitors must sit in the front row. Out of the 8
canoeing competitors,
3 are male; these 3 must sit in the second row. The remaining 15
competitors can sit
wherever they want.
i. In how many ways can the group of competitors be seated for the
photograph?