File Tools View Chapter 10 Introduction to Counting.docx [Compatibility Mode] - Word X 6. Ten members of a wedding party are lining up in a row for a photo- 4. There are 30 boys and 35 girls that try out for a chorus. The choir di- graph. rector will select 10 girls and 10 boys from the children trying out. a) How many ways are there for the wedding party to line up in How many ways are there for the choir director to make his selec- which the bride is not next to the groom? tion?L ( source: Exercise 10.5.5: Choosing a chorus) b) How many ways are there for the wedding party to line up if the groom is not in the leftmost position? 5. A group of five friends go to a restaurant for dinner. The restaurant c) How many ways are there for the wedding party to line up if the offers 20 different main dishes. groom is not at one end (i.e. in the leftmost or rightmost posi- a) Suppose that the group collectively orders five different dishes to tions)? share. The waiter just needs to place all five dishes in the center of (source: Exercise 10.7.4: Lining up a wedding party for a photo) the table. How many different possible orders are there for the group? 7. How many ways are there to deal hands from a standard playing deck b) Suppose that each individual orders a main course. The waiter to four players if: must remember who ordered which dish as part of the order. It's a) Each player gets exactly 13 cards. possible for more than one person to order the same dish. How b) Each player gets seven cards and the rest of the cards remain in the many different possible orders are there for the group? deck? c) Suppose that each individual orders a main course. The waiter ( source: Exercise 10.8.3: Dealing cards to four players) must remember who ordered which dish as part of the order. 8. Sally goes into a candy store and selects 12 pieces of taffy. The candy However the friends agree that no two people will order the same store offers 75 varieties of taffy. How many ways are there for Sally dish. to select her 12 pieces of taffy? (source: Exercise 10.6.5: Counting orders at a restaurant) (source: Exercise 10.9.3: Selecting pieces of taffy) screens 3-4 of 5 - - + 140%File Tools View Chapter 10 Introduction to Counting. docx [Compatibility Mode] - Word X 9. A grandfather is giving away all 45 coins in his coin collection to his nine grandchildren. The coins are all different, and he wants to give the same number of coins to each grandchild. How many different ways are there for him to distribute his collection? (source: Participation Activity 10.10.1: Applying balls in bins formulas in word problems. (#6)) 10. Count the number of binary strings of length 10 subject to each of the following restrictions. a) The string has at least one 1. b) The string has at least one 1 and at least one 0. c) The string contains exactly five 1's or it begins with a 0. (source: Exercise 10.11.2 Counting binary strings) End of document screen 5 of 5 - - + 140%