Engineering Board Exam Reviewer · Combinations · medium
A committee of 4 is chosen from 7 men and 5 women. In how many ways can it be chosen if it must include at least 2 women?
- 210
- 350
- 495
- 285
Answer
D. 285
Solution
Total: 12C4=495. Subtract committees with fewer than 2 women: no women 7C4=35; exactly one woman 5×7C3=175. So 495-35-175=285.
More Combinations questions
- In how many ways can 6 items be chosen from 8 different items?
- A committee of 3 is to be chosen from 12 members. In how many ways can this be done?
- In how many ways can a committee of 4 be selected from a group of 10 people?
- From a standard deck of 52 cards, how many different 5-card hands are possible?
- 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?
- How many diagonals does a decagon (10-sided polygon) have?
- From a standard deck of 52 cards, how many 5-card hands consist entirely of cards from a single suit?
- A basketball team has 12 players. How many different 5-player lineups (position doesn't matter) are possible?
- How many ways can you choose 2 red balls and 3 blue balls from a bag containing 5 red balls and 6 blue balls?
- A test has 12 questions, and a student must answer any 10. In how many ways can the student choose which questions to answer?