Section 4.6. The Counting Principle and Permutations

Section 4.6: The Counting Principle and Permutations Homework: 1) The daily double at most racetracks consists of selecting the winning horse in both the first and the second race. If the first race has 7 entries and the second has 8 entries, how many daily double tickets mush you purchase to guarantee a win? 2) If a club consists of 10 members, how many different arrangements of president, vice-president and secretary are possible? 3) A lock combination consists of three numbers between 0 and 24 inclusive. How many combinations are possible, assume repetition is allowed? 4) A lock combination consists of three numbers between 0 and 24 inclusive. How many combinations are possible, assume repetition is NOT allowed? 5) A social security number consists of nine digits. How many different social security numbers are possible if repetition of digits is NOT permitted? 6) A social security number consists of nine digits. How many different social security numbers are possible if repetition of digits is permitted? 7) A class ring has three stone options (emerald, ruby or sapphire), two metal options (gold and silver). How many different class rings are possible? 8) Anthony has 6 dress shirts and 4 ties. How many shirt and tie outfits can he make? 9) How many different sandwiches can be made with 2 choices of bread, 3 choices of toppings and 2 choices of meat? 10) A batting order must be created from the 9 starters on a baseball team. How many batting orders are possible? 11) A batting order must be created from the 9 starters on a baseball team. How many batting orders are possible if the pitcher must bat last? 12) A batting order must be created from the 9 starters on a baseball team. How many batting orders are possible is a specific person must hit 4th? 13) A batting order must be created from the 9 starters on a baseball team. How many batting orders are possible if the first 4 batters are already assigned? 14) A multiple choice test has 5 questions and each question has 4 choices. How many ways are there to answer the questions? 15) A multiple choice test has 5 questions and each question has 4 choices. How many ways are there to answer the questions if you know the answer to the first question? 16) A multiple choice test has 5 questions and each question has 4 choices. How many ways are there to answer the questions if you know the answer to the first two questions? Homework 17 – 20: an identification code is to consist of two letters followed by 4 digits. How many different codes are possible if 17) Repetition is permitted 18) The first letter must be A, B, C or D and repetition is not permitted? 19) Repetition of numbers is permitted, but repetition of letters is not permitted? 20) Repetition is not permitted? Homework #21-24: a license plate is to consist of three digits followed by two uppercase letters. Determine the number of different license plates possible if 21) Repetition of numbers and letters is not permitted 22) Repetition of numbers and letters is permitted 23) The first digit cannot be a zero, and repetition is not permitted 24) The last digit must be even and repetition is permitted Homework #25-30: Use the permutation of distinct objects formula solve the following 25) How many ways can the letters of Mississippi be arranged? 26) How many ways can the letters of Pennsylvania be arranged? 27) How many ways can the letters x,x,x,y,y,z,z,z,z be arranged? 28) How many ways can the letters a,b,b,b,c,c,c,d,d,e be arranged? 29) How many ways can the letters of abracadabra be arranged? 30) How many ways can the letters of Diamondbacks be arranged? n! to n1 ! n2 ! n3 ! nr ! Answers: 1) 7*8 = 56 3) 25*25*25= 15,625 5) 10*9*8*7*6*5*4*3*2 = 3,628,800 ways 7) 3*2 = 6 9) 2*3*2 = 12 11) 8*7*6*5*4*3*2*1*1 =40,320 13) 1*1*1*1*5*4*3*2*1 = 120 15) 1*4*4*4*4 = 256 17) 26*26*10*10*10*10 =6,760,000 19) 26*25*10*10*10*10 = 6,500,000 21) 10*9*8*26*25 = 468,000 11! 23) 9*9*8*26*25 = 421,200 25) 4!∗4!∗2! = 34,650 27) 9! 3!∗2!∗4! = 1260 29) 11! 5!∗2!∗2! = 83,160