MATH 135 Exam 1 Sample Fall 2019 1 A product code begins with A B or C and this letter is followed by three digits How many product codes are possible if digits are allowed to be repeated but cannot be repeated consecutively For example C973 and B010 are possible product codes but C997 is not A 2160 B 2430 C 2757 D 2970 E 2187 F 2700 2 If and are disjoint subsets of and 12 14 and 30 what is A 22 B 16 C 28 D 14 E 20 F 26 3 If peanut walnut pecan cashew filbert almond peanut filbert walnut peanut cashew walnut and pecan walnut what is A cashew filbert almond peanut B cashew filbert peanut C peanut D cashew filbert almond peanut walnut E peanut pecan walnut F walnut 4 Every weekend Sharon does one of 3 things stay in Bloomington go to Indianapolis to visit her mother or go to Lafayette to visit her boyfriend She wants to plan the next 5 weekends in advance How many different ways are there for her to do this A 8 B 10 C 125 D 60 E 15 F 243 5 A product code consists of either three or four not necessarily distinct letters Only the letters G H X Y and Z can be used For example GGZ and ZXHG are two such product codes If one such product code is selected at random what s the probability it includes the letter H A B C D 43 75 7 10 1 3 76 125 1 E 5 F 11 15 6 Andre is at the animal shelter He is going to adopt a dog and two cats The shelter has four dogs and six cats available for adoption How many different ways can Andre choose who to adopt A 34 B 720 C 60 D 15 E 120 F 19 7 Jack and Jill s favorite ice cream parlor has five flavors of ice cream vanilla chocolate strawberry cookie dough and rum raisin The special today is a three scoop bowl Jack likes variety so he s going to get three different flavors How many different ways can he do this A 60 B 5 C 125 D 12 E 15 F 10 8 Jack and Jill s favorite ice cream parlor has five flavors of ice cream vanilla chocolate strawberry cookie dough and rum raisin The special today is a three scoop bowl Jill doesn t like to mix flavors so she s going to get three scoops of the same flavor How many different ways can she do this A 60 B 5 C 125 D 12 E 15 F 10 9 Andrea is at the animal shelter She is going to adopt either a dog or two cats The shelter has four dogs and six cats available for adoption How many different ways can Andrea choose who to adopt A 34 B 720 C 60 D 15 E 120 F 19 10 The Senate Transportation Committee consists of 3 Democrats and 4 Republicans This committee must elect from its own members a Chairperson and a Vice chairperson who cannot be from the same party How many different ways can they elect them A 21 B 12 C 7 D 24 E 42 F 14 11 A calculus class has five students Anton Beatriz Colin David and Eliza Each class day next week Monday Tuesday Wednesday Thursday and Friday one of the students will give a presentation Each student will only give one presentation If days are assigned to the students at random what s the probability that David presents on Monday and Eliza does not present before Thursday A B 3 10 1 40 3 C 5 2 D 5 E F 16 125 1 10 12 How many different six digit numbers can be made by rearranging the digits of 479797 For example 997774 and 479797 are two such numbers A 12 B 60 C 720 D 90 E 120 F 108 13 A bag contains three 5 bills two 10 bills and one 20 bill Bills are selected from the bag one at a time without replacement and their denomination i e their value noted until the total value of the selected bills is at least 25 How many outcomes does this experiment have A 28 B 115 C 9 D 23 E 6 F 20 14 If and are subsets of a universal set such that 60 2 4 6 8 10 12 14 and what is A 40 B 4 C 20 D 60 E 56 F 2 15 A teacher has five 1st grade students and four 2nd grade students He will select one student from each grade to be the classroom leaders How many different ways can he select these leaders A 9 B 40 C 72 D 20 E 36 F 144 16 A bag contains three 5 bills two 10 bills and one 20 bill If three bills are selected from the bag at random what is the probability that the total value of the selected bills is at least 25 A 13 20 1 B 6 2 C 3 D 13 60 5 E 7 F 5 11 17 Iffy Tech Community College has two kinds of instructors full time and adjunct Each full time instructor teaches five classes and each adjunct instructor teaches two classes Currently there are 30 full time instructors and 90 adjunct instructors If one current class is selected at random what is the probability it has a full time instructor A B 1 3 5 11 1 C 4 5 D 6 E F 2 17 2 45 18 Amber has 6 notebooks She needs to decide which notebooks to take to school today The only requirement is that she must take at least 1 notebook How many different ways could she make the decision A 719 B 6 C 20 D 720 E 5 F 63 19 The diagram below shows the number of elements in each region What is A 3 B 40 C 24 D 10 E 9 F 50 20 If 1 1 1 1 1 2 1 2 2 2 1 what is A 1 B 1 C 2 D 1 E 1 F 1 1 21 Calvin has six different cans of soup He needs to choose three of them to donate to a food bank and one to eat for lunch How many different ways can he do this A 18 B 360 C 1080 D 120 E 60 F 26 22 A set has 7 elements How many different subsets of this set have at least 2 elements A 14 B 189 C 128 D 120 E 13 F 35 23 A set is partitioned into subsets 1 2 3 4 5 and 6 such that 1 2 3 5 6 1 2 4 and 5 2 1 If 300 what is 3 A 50 B 80 C 25 D 100 E 40 F 20 ANSWERS 1 B 2 C 3 D 4 F 5 B 6 C 7 F 8 B 9 F 10 D 11 …