Assignment:
Q1. Given the group {Allen, Brenda, Chad, Dorothy, Eric} you will be asked to determine
a. the number of ways of choosing a president, vice-president and secretary/treasurer. (3 points)
b. the number of ways of choosing a leadership team composed of 2 members. (3 points)
c. the number of ways of choosing a president, vice-president, and secretary/treasurer given the president and secretary must be a female.
Q2. A grocery store is arranging the Coke and Pepsi products for display on one row of shelving. The store carries 5 Coke products (Coke Classic, Diet Coke, Caffeine Free Coke Classic, Spite and Coca-Cola Zero) and 7 different Pepsi products (Pepsi, Diet Pepsi, Pepsi Vanilla, Pepsi Twist, Pepsi Lime, Wild Cherry Pepsi, and Pepsi One). How many different ways can these drinks be arranged so that all of the Coke products are together and all of the Pepsi products are together?
Q3. A company that employees 6 managers, 15 clerical workers and 23 warehouse personnel is relocating and wants to create a committee that has representatives from each group to oversee the process. How many different ways can they select 2 managers, 4 clerical workers and 7 warehouse personnel to serve on this committee?
Provide complete and step by step solution for the question and show calculations and use formulas.