Unit 8 Practice Fall 2008 Station 1 – Counting Principle, Permutations, & Combinations 1) Cindy is playing Scrabble and has the following letter tiles.

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Unit 8 Practice Fall 2008 Station 1 – Counting Principle, Permutations, & Combinations 1) Cindy is playing Scrabble and has the following letter tiles on her tray: A, L, S, T, D, R, L. How many different 7-letter arrangements are possible with the letters? 2) In a standard deck of cards, how many five-card hands are there? 3) Three men and three women are to be selected to represent a group of eleven men and fourteen women. How many ways can the representatives be selected? 4) Three people from a class of 21 will be selected for class president, class secretary and class treasurer. In how many ways can the three positions be determined? 5) Three different hardcover books and five different paperback books are placed on a shelf. How many ways can they be arranged if all the hardcover books must be together? 6) Henry has the choice of the following clothing items: a pair of jeans, a pair of corduroy pants, a striped dress shirt, a solid dress shirt, a polo shirt, sneakers, dress shoes, a black belt, and a brown belt. How many different outfit combinations can he make?

Unit 8 Practice Fall 2008 Station 2 – Introduction to Probability 1) You draw 1 card from a standard deck of cards. Find each probability. a) P(Club)b) P(Odd numbered card) c) P(Ace of Hearts)d) P(Black face card) e) P(A Heart or a Queen)f) P(A Face card or a Diamond) 2) You draw 1 card from a standard deck of cards, then replace it and draw a second card. Find each probability. a) P(Club then a Heart)b) P(Ace then an Ace) c) P(Face card then the Two of Spades)d) P(Five then a Red Ten) 3) You draw 2 cards from a standard deck of cards. Find each probability. a) P(Two 10’s)b) P(Two Diamonds) c) P(Two Black Cards)d) P(Two Face Cards) 4) A jar contains 6 yellow, 8 purple and 5 orange marbles. Find each probability. a) What is the probability of picking a orange, orange, yellow, yellow, then yellow marble in that order. You are picking one at a time with no replacement. b) What is the probability of picking one yellow, then one purple, then one orange. (You are picking them one at a time with replacement). 5) Two dice are rolled. Find the probability of each outcome. a) The sum is at least 7.b) The sum is odd or prime. c) The difference is 2.d) The sum is 1.

Unit 8 Practice Fall 2008 Station 3 – Introduction to Odds 1) Each ratio given represents the probability of an event. Change the ratio into odds. a)b)c)d) 2) Each ratio given represents the odds of an event. Change the ratio into the probability. a)b)d)e) 3) What are the odds of selecting a five at random from a standard deck of cards? 4) What are the odds of rolling an even number on a six-sided die?

Unit 8 Practice Fall 2008 Station 4 – Advanced Probability 1) Two cards are selected at random from a standard deck of cards without replacement. Find the probability of each outcome. a) P(One Diamond and One Heart)b) P(One Queen and One Seven) 2) Three cards are selected at random from a standard deck of cards without replacement. Find the probability of each outcome. a) P(2 Tens and 1 Five)b) P(1 Heart, 1 Spade, and 1 Club) 3) Alex has only 11 songs on his iPod. Six are rock and five are classical. Alex is selecting three songs to listen to before school starts. What is the probability that Alex selects at least two classical songs? 4) Two dice are rolled. Find the probability of each outcome. a) P(3 and 5)b) P(Even and Prime) 5) There are 12 seniors and 10 juniors on the prom committee. If two people are selected at random to be in charge of decorations, what is the probability that at least one of them will be a junior? 6) A class is given a list of 20 study problems from which 10 will be part of an upcoming exam. A students knows how to correctly solve 15 of the problems. Find the probability that the student will be able to correctly answer: a) All 10 questions on the exam.b) Exactly eight questions on the exam. c) At least 7 questions on the exam.