5. A catering service offers 8 appetizers, 10 main courses, and 7 desserts. A banquet committee is to select 3 appetizers, 4 main courses, and 2 desserts. How many ways can this be done? 6. One...

Extracted text: 5. A catering service offers 8 appetizers, 10 main courses, and 7 desserts. A banquet committee is to select 3 appetizers, 4 main courses, and 2 desserts. How many ways can this be done? 6. One serving of banana split contains three scoops of different flavors of ice cream, 3 different syrups, 2 different types of nuts, and with or without whipped cream. How many different ways can a banana split be made if there are 12 ice cream flavors, 8 syrups, and 4 types of nuts to choose from? 7. Suppose 6 female and 5 male applicants have been successfully screened for 5 positions. In how many ways can the following compositions be selected? (a) 5 people regardless of sex. (b) 3 females and 2 males; (c) at least 3 females; (d) 4 females and 1 male; (e) 5 females. 8. How many 4-person committees are possible from a group of 10 people including Francis and Jojo if (a) there are no restrictions? (b) both Francis and Jojo must be in the committee? (c) either Francis or Jojo (but not both) must be in the committee? 9. Awarehouse receives a shipment of 20 computers, of which five are defective. Eight computers are then randomly selected and then delivered to a store. In how many ways can the store receive (a) no defective computer? (b) three defective computers? (c) all five defective computers? 10. A 5-card hand is dealt from a standard 52-card deck. How many ways (a) such hands are possible? (b) contain both a queen and a king? (c) contain 3 face cards and an 8? (d) contain only red cards?