Name (printed):Student ID #:Section # (or TA’s:name and time)CMSC 250 Quiz #12 Wednesday, Apr. 21, 2004Write all answers legibly in the space provided. The number of points p os sible for each question is indicatedin square brackets – the total number of points on the quiz is 30, and you will have exactly 15 minutes tocomplete this quiz. You may not use calculators, textbooks or any other aids during this quiz.Note: you only need to take the answer as far as a mathematical expression including addition, sub-traction, multiplication, division, exponents and factorials.1. [15 pnts.] Assume you have fruit to sell in your fruitstand. You have 7 apples, 4 oranges and 6bananas. Fruit of the same type are indistinguishable from each other.You make a fruit basket to deliver to a friend at the hospital. It has 5 pieces of fruit in it. Answerthe following questions about that fruit basket as suming you filled the fruit basket at random (notthinking about what the friend likes or what would look good in the basket). Assume the order youput the fruit into the basket does not make the basket different.a. How many different baskets can be created with the criteria above?b. What is the probability that all of the fruit in the basket are apples?c. Assuming you must have at least one of each type of fruit in the basket, how many differentbaskets could be formed?d. Assume your friend received 2 baskets where the first basket has has 3 apples and 2 orangesand the s econd basket has 2 apples and 3 bananas. Your friend lines up the fruit in a straitline to decide in what order to eat them. How many different linear arrangements can he makeassuming the fruit of the same type is indistinguishable?2. [15 pnts.] Assume you have 27 indistinguishable chocolate candy bars and 5 distinguishable friends.Your friends want you to s hare the candy bars with them. Each of the questions is separate from theothers - any conditions mentioned in one ques tion do not carry to any of the others.Note: you only need to take the answer as far as a mathematical expression including addition,subtraction, multiplication, division, exponents and factorials.a. How many ways can you distribute the candy bars among yourself and your 5 friends?b. You don’t want any of your friends (or yourself) to be left out of the candy bar eating so yourecalculate - how many ways are there to distribute the candy bars among yourself and yourfive friends assuming you want to be sure that each person gets at leas t two candy bars?c. You decide these c andy bars are small so instead of each person receiving at least two asmentioned in the previous question, you want to be sure you and each of your friends eachreceive at least 5 candy bars. Now, how many ways to distribute the candy bars?d. Bill one of the friends is allergic to chocolate, so you need to make sure he do es not receiveany of the candy bars. Now how many ways are there to distribute them? (remember ignorerestrictions in previous questions)e. Since Bill is allergic to chocolate and can’t eat the candy bars, you will add 12 peppermintcandycanes to the candy you are distributing. How many ways can you distribute the candyassuming Bill can not eat the chocolate candy bars, but he can eat the peppermint
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