Probability with Combinations and Permutations Answers

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

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 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?

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?

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.

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 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?

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 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.

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.