Section 4 - 5: Counting Techniques A whole number with the specified number of digits is to be made using the digits in Set A Set A = { 1 , 3 , 4 , 6 , 8 , 9 } 1A. How many 3 digit numbers can be made with the numbers in Set A if no number can be repeated? 1B. How many 4 digit numbers can be made with the numbers in Set A if no number can be repeated? 1C. How many 6 digit numbers can be made with the numbers in Set A if no number can be repeated? 1D. How many 4 digit numbers can be made with the numbers in Set A if any number can be repeated? 1E. How many 3 digit numbers can be made with the numbers in Set A if you can only use even numbers. The even numbers can be repeated? 1F. How many 4 digit numbers can be made with the numbers in Set A if you can only use odd numbers. The odd numbers cannot be repeated?A license plate is to be made that has Alphanumeric Characters taken from Set B. Set B = { 1 , 2 , 3 , 4 , A , B , C } 2A. How many 5 character license plates can be made with the characters in Set B if none of the characters can be repeated? 2B. How many 6 character license plates can be made with the characters in Set B if none of the characters can be repeated? 2C. How many 5 character license plates can be made with the characters in Set B the first character must be a letter and the last character must be a a prime number. None of the characters can be repeated? 2D. How many 4 character license plates can be made with the characters in Set B if the first two characters must be a number and none of the characters can be repeated ? 2E. How many 4 character license plates can be made with the characters in Set B if the first two characters must be a letter and none of the characters can be repeated? 2F. How many 4 character license plates can be made with the characters in Set B if the first two characters must be an even number and none of the characters can be repeated ?3. A computer password is to be made with alphanumeric characters taken from Set C. Set C = { D , E , A , P , 1 , 2 , 3 , 4 ,5 } 3A. How many 7 character passwords can be made that start with a letter, and end with an even number if none of the characters can be repeated ? 3B. How many 6 character passwords can be made that start with a letter, and end with a prime number if none of the characters can be repeated? Note: The prime number are 2, 3, 5, 7, 11,13, 17,19,23, ... 3C. How many 5 character passwords can be made if the first two characters must be odd numbers and the last two characters are letters? No characters can be repeated. 3D. How many 7 character passwords can be made that start with a letter, end with a letter and have a letter in the middle if no characters can be repeated? 4. How many different 6 letter words (real or Imaginary) can be formed from the word RANDOM if no letters can be repeated ?5. A restaurant has the following choices for a three course meal. How may different meals can be selected if you must select one Appetiser, one Entree and one Dessert ? Appetiser = { Soup or Salad } Entree = { Chicken, Steak, Shrimp, Pork Chop, or Tofu } Dessert = { Cheese Cake, Cream Puffs or Ice Cream } 6. A UPS driver has to deliver packages to 7 different houses. How many different delivery paths are possible for the driver to deliver the packages to all 7 houses if the driver can only visit each home one time? 7. A music file has 8 songs stored in it. One song is played without repeats until they are all played. In how many different ways can the songs be played? 8. 15 people volunteered to serve on a three member committee. One will be the President, one will be the Vice President, and one will be the Treasurer. No one can serve in more than one position. How may different committees can be formed? 9. A pin number for your credit card is in the form XXXX where each X is a single digit number. The digits can be repeated. How many different pin numbers can exist? The single digits are 0, 1, 2,3 4, 5,6 7,8 and 9.10. Student ID numbers have 5 characters in the form XX - YYY where each X is a single letter from the alphabet that cannot be repeated. Each Y is a single digit that cannot be repeated. How many different Student ID Numbers can exist? 11. Companies on the National Association of Securities Dealers Automated Quotations can have their company names listed using either four OR five letters. Letters can be repeated. What is the largest number of possible company listings that the Association can have? Igno smort 12. Companies on the New York Stock Exchange can have their company names listed using either a one, two or three letters from the alphabet. Letters can be repeated. What is the largest number of possible listings that the Exchange can have? 13. Of all the three character passwords the can be made from the characters in Set W ( the characters CAN be reused ), what is the probability that I have a three character password that starts with a letter and ends with a number? Set W = { B , D, L , M , 1 , 2 } 14. Of all the four character passwords the can be made from the characters in Set W ( the characters CANNOT be reused ), what is the probability that I have a four character password that starts with a letter and ends with a number? Set W = { B , D, L , 1 , 2 }15. Of all the five character passwords that can be made from the characters in Set W ( the characters CANNOT be reused ), what is the probability that it is a five character password that starts with a letter and end with an even number and has an odd number in the middle? Set W= { B , D, L , 1 , 2 . 3, 4 } 16. Of all the three letter words (real or Imaginary) that can be made using the English alphabet (the words can have repeated letters in them), what is the probability that I if select one of the three letter words described above it will start with one of the following letters: A, E, I, O, U? 17. Of all the four letter words (real or Imaginary) that can be made using the English alphabet (the words cannot have repeated letters in them), what is the probability that I select one of the four letter words described above and the word starts an M or an O. 18. Of all the four letter words (real or Imaginary) that can be made using the English alphabet (the words cannot have repeated letters in them), what is the probability that it has an M first and an A second