3.44: Choosing 5 people with restrictions

0606/21/O/N/21 — Question 8 · 7 marks

Marc chooses 5 people from 4 men, 4 women and 2 children.
(a)
Find the number of ways if there are no restrictions.
[1]
(b)
Find the number of ways if at least 2 men are chosen.
[3]
(c)
Find the number of ways if at least 1 man, 1 woman and 1 child are chosen.
[3]