Exercise Set 7.3: Permutation or Combination? First decide whether order matters. Then find the number of possibilities for the given situation. 1. How many different 5-card poker hands are possible from a deck of 52 cards? 2.
There is a raffle to be held in a classroom of 24 students. If 5 prizes are to be raffled, how many sets of winning students could there be?
3. There are 13 of each suit in a deck of 52 cards. How many 5-card hands have all the same suit? 4. There are 9 candidates in a city election for mayor. The winner will be the mayor, and the runner-up will be the vice mayor. How many different cabinets of mayor and vice-mayor are possible? 5. At Baskin-Robbins there are 31 flavors of ice cream to choose. How many different ways are there to select 3 flavors to put into a cup? 6. At Baskin-Robbins there are 31 flavors of ice cream to choose. How many different ways are there to select 3 flavors to put onto a cone? 7. A train is to be made up of a locomotive, 7 different cars, and a caboose. If the locomotive must be first, and the caboose must be last, how many ways can the train be ordered? 8. A bracelet is to be made up of a clasp, 10 different charms, and a fastener. If the clasp must be at one end, and the fastener at the other, how many ways can the charms be ordered?
9. Brian and David are among 15 students who have applied for a trip to a leadership conference for the summer. Two students from the group will be selected at random for the trip. How many different ways can two students be selected for the trip? 10. A Scrabble bag toward the end of a game only contains 4 A’s, 3 E’s, and 5 R’s. If you can only draw 3 letters, how many sets of letters are possible for your draw? 11. You are almost done playing Words with Friends, and you have only 5 letters remaining. How many different ways can you arrange the letters in order to figure out a word for your next move? 12. The Trifecta is a bet made in horse racing to pick the first, second, and third place horses in a race. Eight horses run in a single race. In how many different ways can these horses come in first, second, and third? Assume that there are no ties. 13. The Superfecta is a bet made in horse racing to pick the first, second, third, and fourth place horses in a race. Eight horses run in a single race. In how many different ways can these horses come in first, second, third, and fourth? Assume that there are no ties. 14. In how many distinct ways can the letters in the word CRAZY be written? 15. In how many distinct ways can the letters in the word HORSE be written? 16. You are the team captain of a swim team. You must form a 12-member swim team from 15 girls and 18 boys. The team must consist of 5 girls and 7 boys. How many different 12-member teams are possible?
