WIR Math 166-copyright Joe Kahlig, 10A Page 1Week in Review #4Section 2.2: Combination• p ermutation of distinct objects: P (n, r) =n!(n−r)!where r ≤ narrangement of r objects from a set of n objectswith 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,... for a total of n objects.• combination: C(n, r) =n!(n−r)!r!where r ≤ na group of r objects from a set of n objectswith order not being important.1. A box has 4 red, 7 green, and 8 yellow balls. How many ways can a samp le of 6 balls be selected fromthe box that contains(a) exactly 2 red and exactly 4 green balls.(b) exactly 2 red balls.(c) at least 2 green balls.(d) exactly 2 red balls or exactly 4 yellow balls.(e) exactly 2 red b alls or exactly 3 green balls.2. A meal at a local restaurant consists of a m ain dish, two vegetable dish es, and a desert. If there are 10main dishes, 13 vegetable dishes, and 8 deserts, how many different meals are possible?WIR Math 166-copyright Joe Kahlig, 10A Page 23. A basketball program has 20 kids signed up to play in a summer league. How many ways can these kidsbe divided into teams of 5 to be coached by 4 different coaches.4. How many different arrangements are there of the letters of th ese words?(a) representation(b) Endangered5. The Student Senate is creating a committee to stud y the issue of professors parking in the student lots.This committee will consists of 5 senators with one designated the chairperson and another designatedthe assistant chairp ers on . Currently 9 senators want to be on the committee. How many committees arepossible?6. A group has 8 guys and 10 girls as its members. In how many ways can 3 of the guys and 5 for the girlsstand in a r ow for a picture?7. How many ways can you get these poker hands? (note: this is a 5 card hand)(a) full house (ex JJJ33)(b) two pairs (ex JJKK2)WIR Math 166-copyright Joe Kahlig, 10A Page 3Section 2.3: Probability applications of Counting Principles• If S is an uniform sample space• P (E) =n(E)n(S)• n(E) is the number of ways to get what we want.• n(S) is the number of possible outcomes in S.8. Fifteen cards are numbered 1 through 15. The cards are shuffled, and three cards are drawn and arrangedin a row.(a) Find the probability that the first is odd and the second is even.(b) Find the probability that the first two are odd, and th e third is an even number greater than 9.9. David is selecting 10 kids from a group of 30 kids to form a summer basketball team. The group of 30 kidsis made up of 9 thirteen-year-olds, 13 fourteen-year-olds, and 8 fifteen-year-olds. What is the probabilitythat exactly 3 kids that are fifteen-years-old were selected on the team.10. Three couples are going to an Aggie football game. They have tickets next to each other all in the samerow. If the tickets are randomly given to the 6 people, what is the probability of each couple standingtogether?11. Jim is taking an exam where he has to answer 10 of the 15 question on the exam. What is the probabilitythat Jim answers at most 4 of the first 7 questions?WIR Math 166-copyright Joe Kahlig, 10A Page 412. A committee of 6 students are to be chosen from a group of 9 freshmen, 10 sophomores, and 7 juniors.Find the probability that(a) The committee has all sophomores.(b) The committee has a majority of freshmen.(c) Bill, Sue, Sara and Jim are on the committee.(d) Only two of Bill, Sue, Sara and Jim are on the committee.13. Your 4 year old nephew is playing with some blocks. The blo cks are identical except for the letter onthe block: one block has an M, four blocks have an I, 4 blocks have an S, and 2 blocks h ave a P. If yournephew places all of the blocks in a row, what is the probability that he spells the word MISSISSIPPI?14. Fifteen people are all applying for thr ee different scholarships. What is the probability that John, who isone of th e 15 people, get at least 2
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