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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.

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