This is a question in discrete math and requires us to find the actual number of ways for these scenarios. 3. Seven numbered red balls and three indistinguishable blue balls are to be placed in five...

This is a question in discrete math and requires us to find the actual number of ways for these scenarios.

3. Seven numbered red balls and three indistinguishable blue balls are to be placed
in five labelled boxes.
(a) What is the number of placements with the condition that each box contains
at least one red ball?
(b) What is the number of placements where each box contains at most one blue
ball and none of the boxes are left empty?