WIR Math 141-copyright Joe Kahlig, 08A Page 1Week in Review #5Section 6.2: The number of elements in a Finite Set.• n(A) denotes the number of things in set A.• n(φ) = 0• Set A and B are disjoint provided that A ∩ B = φ• A and B are any two sets.• n(A ∪ B) = n(A) + n(B) − n(A ∩ B)• A, B, and C are any three sets.• n(A ∪ B ∪ C) = n(A) + n(B) + n(c) − n (A ∩ B) − n(A ∩ C) − n(B ∩ C) + n(A ∩ B ∩ C)1. A group of 160 students were asked which of these sports they participated in high school.15 students participated in all of these sports25 students participated in basketball and track.25 students participated in basketball and Tennis b ut not track.15 students participated in track but not tenn is.70 students participated in basketball.100 students did not participate in tennis.37 students participated in exactly one sport.(a) Fill in the Venn diagram.(b) How many students participated in track?(c) How many stu dents participated in at least two sports?(d) How many students participated in basketball or tennis but did not participate in track?WIR Math 141-copyright Joe Kahlig, 08A Page 22. A group of students were asked which of these types of pets: dogs, cats, or fish, they had w hen they werekids.28 said they only had a dog.6 said they had all three of these pets.16 said they had a dog and a fish.15 said they had a fish but did not have a cat.48 said they only had one of these types of pets when they were a kid.57 said they had fish or a cat as a pet when they were a kid.87 said they did not have a fish as a pet when they were a kid.57 said they did not have a dog as a pet when they were a kid.(a) Fill in the Venn diagram.(b) How many students were in the survey?Section 6.3: The multiplication Principle.3. Four processes are involved in assembling a produ ct an d can be performed in any order. Th e managementwants to test each ord er to determine which is the least time consuming. How many different orders willhave to be tested?4. An exam consists of 3 true false questions followed by 5 multiple choice questions each with 4 answers.How many ways can the exam be answered assuming that no questions are left blankWIR Math 141-copyright Joe Kahlig, 08A Page 35. John, Sue, Beth and 3 other fr iends are lining up for a picture. How many ways can all of them line upto take the picture if Sue has to be directly between John and Beth?6. Bob has designed a five-symbol license plate for the vehicles at a local theme park that use either allletters or two letters followed by three digits.(a) How many license plates are possible if the first letter must be a M, E, or W?(b) How many license p lates are possible if the first letter must be a M, E, or W and no letter or digitcan be r epeated?Section 6.4: Permutations and Combinations• permutation of distinct objects: P (n, r) =n!(n−r)!where r ≤ n• arrangement of r objects from a set of n objects with order being important.• permutation of not all distinct objects:n!n1!n2!n3!...nr!• n1+ n2+ n3+ ... + nr= n where n1objects are alike and one of a kind, n2objects are alike and one of a kind,...• combination: C(n, r) =n!(n−r)!r !where r ≤ n• a group of r objects from a set of n objects without regard to order.7. A box has 4 red, 7 green, and 8 yellow balls. A sample of 6 objects will be selected from the box. Howmany ways can a sample of 6 b alls be selected from the box that contains(a) exactly 2 red and exactly 4 green b alls.(b) exactly 2 red balls.(c) at least 2 green balls.WIR Math 141-copyright Joe Kahlig, 08A Page 4(d) exactly 2 red balls or exactly 4 yellow balls.(e) exactly 2 red balls or exactly 3 green balls.8. A meal at a local restaurant consists of a main dish, two vegetable dishes, and a desert. If there are 10main dish es, 13 vegetable dishes, and 8 deserts, how many different meals are possible?9. How many ways can a group of 10 people have their birthdays on different days of the year? Assumethat there are only 365 d ays in a year.10. A b asketball program has 20 kids signed up to play in a sumer league. How many ways can these kidsbe divided into teams of 5 to be coached by 4 different coaches.11. How many different arrangements are there of the letters of the word
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