Combinations — Engineering Board Exam Practice Questions

8 free engineering board exam reviewer questions on Combinations (Combinatorics and Probability), each with the correct answer and a worked solution.

1. In how many ways can a committee of 4 be selected from a group of 10 people?
2. From a standard deck of 52 cards, how many different 5-card hands are possible?
3. A committee of 5 is to be chosen from 6 men and 4 women. How many committees will have exactly 3 men and 2 women?
4. How many diagonals does a decagon (10-sided polygon) have?
5. From a standard deck of 52 cards, how many 5-card hands consist entirely of cards from a single suit?
6. A basketball team has 12 players. How many different 5-player lineups (position doesn't matter) are possible?
7. How many ways can you choose 2 red balls and 3 blue balls from a bag containing 5 red balls and 6 blue balls?
8. A test has 12 questions, and a student must answer any 10. In how many ways can the student choose which questions to answer?