Which of the following scenarios describes a combination?

Assigning a president, vice-president, and secretary from a club of 20 members.

Creating a 3-letter passcode using the letters A, B, C, and D without repetition.

Selecting 5 books to read from a list of 12 for a summer reading assignment.

Awarding gold, silver, and bronze medals to the top three finishers in a race.

Solving Problems Involving Combinations Practice — Grade 9 math

Lesson 118: Solving Problems Involving Combinations — Practice Questions

1. An art teacher needs to select 4 students from a group of 9 to display their work. How many different groups of 4 students can be chosen? The answer is ___.
2. If the number of permutations of choosing 3 items from a set of 7 is $_7P_3 = 210$, what is the correct way to find the number of combinations, $_7C_3$?
- A. Multiply 210 by 3
- B. Divide 210 by 3!
- C. Multiply 210 by 7!
- D. Divide 210 by 7
3. A game developer is choosing 3 different bonus items from a list of 10 possible items to include in a treasure chest. How many unique combinations of bonus items are possible? The answer is ___.
4. Which of the following scenarios describes a combination?
- A. Assigning a president, vice-president, and secretary from a club of 20 members.
- B. Creating a 3-letter passcode using the letters A, B, C, and D without repetition.
- C. Selecting 5 books to read from a list of 12 for a summer reading assignment.
- D. Awarding gold, silver, and bronze medals to the top three finishers in a race.
5. From a group of 8 volunteers, a coordinator needs to form a committee of 3. How many different committees can be formed? The answer is ___.
6. A student must choose 4 books to read from a list of 11. How many different sets of books can the student choose? ___
7. A pizzeria offers 10 toppings. Which expression finds the number of ways to create a 4-topping pizza, if toppings cannot be repeated and order doesn't matter?
- A. $_ {10}P_4 = \frac{10!}{(10-4)!}$
- B. $_ {10}C_4 = \frac{10!}{4!(10-4)!}$
- C. $10 \times 4$
- D. $\frac{10!}{4!}$
8. From a group of 13 job applicants, 11 will be selected for an interview. How many different groups of 11 can be chosen? ___
9. From 8 different prizes, a contestant can choose 3 to take home. How many different combinations of prizes can the contestant choose?
- A. 56
- B. 336
- C. 24
- D. 84
10. There are 8 people in a meeting. If everyone shakes hands with everyone else exactly once, how many total handshakes occur? ___