Probability with Combinations and Permutations Answers

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 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.

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.

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?

Two children are playing a code-breaking game. One child makes a sequence of three colors from red, yellow, blue, and purple. The other child must guess the sequence of colors in the correct order. Once one color is used, it cannot be repeated in the sequence.

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?

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?