I need help with the following problem: There are $3$ groups of people: Group $A$ of $4$ people, Group $B$ of $5$ people, Group $C$ of $6$ people. In how many ways can these people receive $5$ identical rewards if...
- At Least $2$ people from group $B$ and at least $2$ people from group $C$ must receive a prize.
- At least one person from each group must receive a reward, but no more then $2$ people from one group.
I know that the answer to 1. is $950$ and the answer to 2. is $1410$, but I would really like an explanation.