b) How many families were surveyed? c) How many families brought costumes?

Transcription

1 Name: Math 1324 Activity 15(Due by EOC Nov. 15) Dear Instructor or Tutor, These problems are designed to let my students show me what they have learned and what they are capable of doing on their own. Please allow them to work the problems on their own! If you would like to help them with similar problems, here are the related homework problems: pg. 374: 7-31 odd, odd, 49, 51, pg. 386: 7-25 odd, 37, 39, odd, 61, 65, 71, 75. Thanks! Dear Student, Don t even think about asking for help on the problems in this activity! The recommended homework problems have answers in the book, so do them first for practice!!! 1. At a powwow in Arizona, Native Americans from all over the southwest came to participate. A survey gave the following results: 15 families brought food, costumes, and crafts 25 families brought food and crafts 42 families brought food 20 families brought costumes and food 6 families brought costumes and crafts, but not food 4 families brought crafts, but neither food not costumes 10 families brought none of the three items 18 families brought costumes but not crafts. a) Complete the Venn diagram. Food Costumes 15 Crafts 10 b) How many families were surveyed? c) How many families brought costumes? d) How many families brought crafts, but not costumes? e) How many families did not bring crafts? f) How many families brought food or costumes? g) How many families brought food and crafts, but not costumes?

2 2. The number of female military personnel on active duty is given in the following table: Army(A) Air Force(B) Navy(C) Marines(D) Total Officers(O) 10,671 11,662 7, ,045 Enlisted(E) 61,871 54,537 43,010 9, ,805 Total 72,542 66,199 50,771 10, ,850 Use this information to determine the number of female military personnel in each of the following sets: a) A B b) E C D c) O B d) B C e) A B C D f) O E g) B O h) O D i) O E 3. How many different heating-cooling units are possible if a homeowner has 3 choices for the efficiency rating of the furnace, 3 options for the fan speed, and 6 options for the air condenser? 4. How many different 4-letter radio station call letters can be made if a) the first letter must be K or W and no letter may be repeated? b) the first letter must be K or W and repeated letters are allowed? c) How many of the 4-letter call letters in part a) end in R? d) How many of the 4-letter call letters in part b) end in R?

3 5. For many years, the state of California used 3 letters followed by 3 digits on its automobile license plates. a) How many different license plates are possible with this arrangement? b) When the state ran out of new numbers, the order was reversed to 3 digits followed by 3 letters. How many new license plates were then possible? c) Several years ago, the numbers described in part b) ran out. The state then issued plates with 1 letter followed by 3 digits and then 3 letters. How many new license plates will this provide? 6. From a cooler with 8 cans of different kinds of soda, 3 are selected for 3 people: Andrea, Bob, and Carlos. In how many different ways can this be done? 7. Four items are to be randomly selected from the first 25 items on an assembly line in order to determine the defect rate. How many different samples of 4 items can be chosen? 8. From a group of 15 smokers and 21 nonsmokers, a researcher wants to randomly select 7 smokers and 6 nonsmokers for a study. In how many different ways can the study group be selected? 9. A concert is to consist of 8 works: 3 overtures, 3 sonatas, and 2 piano concertos. a) In how many different ways can the concert be arranged? b) In how many different ways can the concert be arranged if an overture must be first? c) In how many different ways can the concert be arranged if works of the same type must be together?

4 10. One play in a state lottery consists of choosing 6 distinct numbers from 1 to 44. If your 6 numbers are selected, you win the jackpot. a) How many different ways are there to select the 6 numbers? b) If you get 2 plays for a dollar, what is the least cost to guarantee that 1 of your choices would be selected? 11. A shipment of 8 computers contains 3 with defects. How many samples of the following size will not contain a defective computer. a) 2 b) Two cards are drawn at random from an ordinary 52-card deck. a) How many different 2-card hands are possible? b) How many 2-card hands consist of 2 kings? c) How many 2-card hands consist of 2 face cards? d) How many 2-card hands contain at least 1 black card?

5 13. A car dealer has 6 red, 10 gray, and 7 blue cars in stock. Ten cars are randomly chosen to be displayed in front of the dealership. How many different ways can it be that a) 4 are red and the others are blue b) 3 are red, 3 are blue, and 4 are gray c) exactly 5 are gray and none are blue d) all 10 are gray e) none are gray f) at least 1 is gray g) at most 2 are gray h) at least 2 are gray Bonus#1: Find the ones digit of Bonus#2: What is the ones digit of 9999! 9998! 9997! 9996! 3! 2! 1!?

6 Bonus#3: Why should you never let a mathematician set your hair? Match your answers to the following problems with the lettered answers below, and write the letter in the corresponding box at the bottom to get the answer to the riddle. 1) 7 P 3 2) 7 P 4 3) 7 4) 7 C 4 5) 4 P 7 6) 7 P 7 7) 7 C 7 8) 7 P 1 9) 7 C 1 10) 7 C 0 11) How many permutations of the letters VWXYZ are there? 12) How many different 5-letter words with repetition can be formed from the letters VWXYZ? 13) How many different 3-letter words without repetition can be formed from the letters VWXYZ? 14) How many different 3-letter words with repetition can be formed from the letters VWXYZ? 15) How many different subsets of size three are there from the set V, W, X, Y, Z? 16) In a class of 24 students, how many ways could a first, second, and third prize be awarded if no student can be awarded more than one prize? 17) In a class of 24 students, how many different committees of size 3 can be chosen? 18) In a class of 14 boys and 10 girls, how many different committees of size 6 consisting of 3 boys and 3 girls can be chosen? 19) In a class of 14 boys and 10 girls, how many different 3-person committees are of the same gender? 20) How many different ways can a class of 24 students line up? 21) How many different permutations of the letters in the word DADDY are there? 22) How many different permutations of the letters in the word STATISTICS are there? A. 1 B. 6 E. 210 M. 35 N. 343 O P. 24 T. 7 U. 840 W. 823,543 X Y. 0 3 A. 5 5 C. 3 5 E. 5 G. 5! I. 24! K. 10! M. 5 P 3 N. 5 O. 5! 10! P. R. 24 P 3 T. 24 U ! 3! 3! 2! C C Y