Example 2: Among a set of 5 black balls and 3 red balls, how many selections of 5 balls can be made such that at least 3 of them are black balls.
Solution: Selecting at least 3 black balls from a set of 5 black balls in a total selection of 5 balls can be
- 3 B and 2 R
- 4 B and 1 R and
- 5 B and 0 R balls.
Therefore, our solution expression looks like this.
5C3 3C2 + 5C4 3C1 + 5C5 * 3C0 = 46 ways