Probability with Combinations and Permutations Answers

A standard deck of 52 playing cards contains 13 cards in each of four suits: diamonds, hearts, clubs, and spades. Two cards are chosen from the deck at random.What is the approximate probability of choosing one club and one heart?

Two unique letters are chosen at random from the alphabet.What is the approximate probability that the first letter chosen is A?

At a high school, students can choose between three art electives, four history electives, and five computer electives. Each student can choose two electives.Which expression represents the probability that a student chooses an art elective and a history elective?

Six sophomores and 14 freshmen are competing for two alternate positions on the debate team.Which expression represents the probability that both students chosen are sophomores?

A bag contains 10 red marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. Five marbles are drawn from the bag.What is the approximate probability that exactly two of the five are blue?

Six girls and four boys have entered the science fair. First, second, and third place awards are to be given out.What is the probability that a girl wins the first place award while boys will receive the second and third place awards? Express your answer as a percent.

The track team gives awards for first, second, and third place runners. There are 10 students from school A and 12 students from school B competing.Which expression represents the probability that all three awards will go to a student from school B?

A restaurant offers three vegetable side dishes, two fruit side dishes, and five grain-based side dishes. Each entree comes with two side dishes.What is the approximate probability of randomly choosing one vegetable and one grain-based side dish?

A standard deck of 52 playing cards contains four of each numbered card 2–10 and four each of aces, kings, queens, and jacks. Two cards are chosen from the deck at random.Which expression represents the probability of drawing a king and a queen?

A lock is opened using a sequence of three numbers. The numbers range from 0 to 39, inclusive, and cannot be repeated within the sequence.What is the probability that all the numbers in the sequence are even? Express your answer as a percent and round to the nearest whole number.

Two boys and three girls are auditioning to play the piano for a school production. Two students will be chosen, one as the pianist, the other as the alternate.What is the probability that the pianist will be a boy and the alternate will be a girl? Express your answer as a percent.

A student wants to check six websites. Four of the websites are social and two are school-related. After checking just two sites, she has to leave for school.What is the approximate probability that she checked a social website first, then a school-related website?

A student must choose to participate in two different events during field day. There are four track events, two academic events, and six team sports events.What is the approximate probability that the student will choose to participate in two team sports?

A landscaper is selecting two trees to plant. He has five to choose from. Three of the five are deciduous and two are evergreen.What is the probability that he chooses trees of two different types? Express your answer as a percent.