10.3. Sum Rule

Try these first

1. 1.

   How many ways can you choose a single member from a group of 5 students and 3 faculty?

   Hint

   Add the two groups' counts together.

2. 2.

   A school has 10 basketball players and 4 soccer players. How many ways to choose one player?

   Hint

   Consider only selecting one player from each sport.

3. 3.

   What is the total number of ways to choose one committee member from 6 students and 4 faculty?

   • 10
   • 12
   • 6

   Hint

   Add the available representatives together.

4. 4.

   True or False: The Sum Rule applies to cases where scenarios overlap.

   • True
   • False

   Hint

   Remember that we cannot have overlaps.

5. 5.

   A password requires either 6, 7, or 8 characters. Each character can be either a digit, uppercase letter, or a special character. How many valid passwords can be formed given that the count of digits must be at least one?

   Hint

   Use Product Rule first to find total possible combinations, and subtract invalid ones.

6. 6.

   In a survey, if 50 people prefer coffee, 20 prefer tea, and both groups dislike each other, how many distinct preferences can be counted?

   Hint

   Always check if the groups can be simultaneously counted before summing.