Solving Probability Problems by Using Combinations Section 10

First Example Ten red balls and four blue balls are in a bag. If four balls from the bag are to be selected at random (without replacement), determine the probability of selecting four red balls.

Drawing Aces Determine the probability of being dealt 3 aces from a standard deck of 52 cards when 3 cards are dealt.

Faculty-Student Committee A committee of four is to be randomly selected from a group of seven teachers and eight students. Determine the probability that the committee will consist of two teachers and two students.

Theater Seating Five men and six women are going to be assigned to a specific row of seats in a theater. If the 11 tickets for the numbered seats are given out at random, determine the probability that 1. 2. 3. 4. 5. Five women are given the first five seats next to the center aisle. None of the women are in one of the first five seats. At least one woman is in one of the first five seats. Exactly one woman is in one of the first five seats. Three women are seated in the first three seats and two men are seated in the next two seats.

Dead Man’s Hand What is the probability of being dealt a dead man’s hand (i. e. , a pair of aces, a pair of eights, and another card that isn’t an ace or an eight) when 5 cards are dealt, without replacement, from a standard deck of 52 cards?

Comedy Show Five comedians (Joe, Beth, Seth, Luke and Daria) are planning a show featuring themselves. They decide to choose the order of the performances randomly. What’s the probability that Joe will be the second to perform?

Coin Tosses If you are flipping a coin 10 times in a row, what’s the probability that exactly 6 of those tosses are heads?