Assignment:
Q1. A computer lab contains the following computers – a Hewlett Packard, a Compaq, a Sony, a Dell and 3 different models of Macs. How many different ways can the 7 computers be arranged so that the Macs are all together? (You may assume the computers are all in one line.)
Q2. A public pool employs 17 lifeguards of which 4 are WSI certified. Due to the size of the pool, two of the guards on duty at any given time must be WSI certified. If pool policy is to have a total of 6 guards on duty at any given time, in how many different ways could the 6 be chosen?
Q3. Given the group {Allen, Brenda, Chad, Dorothy, Eric, Fred, Gail} you will be asked to determine
a. the number of ways of choosing a president, vice-president, secretary and treasurer.
b. the number of ways of choosing a leadership team composed of 3 members.
c. the number of ways of choosing a president, vice-president, secretary and treasurer given the president and secretary must be a female.
Provide complete and step by step solution for the question and show calculations and use formulas.