Question

In a beg with 8 red balls and 11 blues balls how
many 5 balls boxes can be chosen those have 4
blue balls?

Answer 1

In a beg with 8 red balls and 11 blues balls how
many 5 balls boxes can be chosen those have 4
blue balls?

Answer 2

If the box has 4 blue balls, then that means the one remaining ball is red.

So, there is only one way to have a 5-ball box with 4 blue balls: It must have one red and 4 blues.

That is if all the balls of a color are identical. If they are somehow distinguishable, then there are

8 ways to choose the red ball
11C4 = 330 ways to choose the blue balls.

That would make 2640 ways to fill a 5-ball box with one red and 4 blue balls.