# Combinations and Permutations

11. 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.)

12. 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?

13. 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.

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11. 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.)

You can consider all 3 different models of Macs as a computer, then there are 5! possible ways to arrange them. Then 3 different models of Macs can change the positions, there are 3! Possible ways to do that. So, ...

#### Solution Summary

Combinations and permutations are investigated. How many different computers can be arranged so that the Macs are all together.