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Combinations and Probability
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Combination Problem: What is the probability of drawing 2 aces from a standard deck of 52 cards without replacement?
Probability Solution: The probability is or approximately 0.00452.
Combination Problem: If 3 students are to be selected from a class of 30 for a trip, how many different groups of students can be formed?
Probability Solution: There are 4,060 different groups possible.
Combination Problem: How many ways can you choose a committee of 4 people from a group of 10?
Probability Solution: There are 210 ways to choose the committee.
Combination Problem: From a class of 15 girls and 10 boys, how many ways can you form a group of 4 students with at least one boy?
Probability Solution: There are 5,005 ways to form such a group.
Combination Problem: In a lottery, 5 numbers are drawn from a set of 50. What is the probability of guessing all the numbers correctly?
Probability Solution: The probability is .
Combination Problem: What is the probability of having exactly 3 heads in 5 flips of a fair coin?
Probability Solution: The probability is or 0.3125.
Combination Problem: During a raffle, 2 prizes are given out and no person can win twice. If 100 tickets are sold, what is the probability that you win both prizes if you purchase one ticket?
Probability Solution: The probability is .
Combination Problem: Given 6 different books, how many ways are there to select 3 books to fit into a bag?
Probability Solution: There are 20 ways to select the books.
Combination Problem: If you have 8 different gifts to give away to 4 friends, how many ways can you distribute the gifts?
Probability Solution: There are 1,680 ways to distribute the gifts.
Combination Problem: How many ways can you arrange 3 red, 4 green, and 5 blue marbles in a row if marbles of the same color are indistinguishable?
Probability Solution: There are 27,720 ways to arrange the marbles.
Combination Problem: A password consists of 2 letters followed by 2 digits. How many unique passwords can be created if letters and digits cannot be repeated?
Probability Solution: There are 67600 unique passwords possible.
Combination Problem: A soccer team of 11 players needs to be formed from a pool of 16 players. How many ways can the team be formed?
Probability Solution: There are 4,368 ways to form the team.
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