Wk5 CT#1 Mathematical: Counting Principles Work through the question below and d

Question

Wk5 CT#1 Mathematical: Counting Principles

Work through the question below and describe or define the Fundamental Counting Principle, combinations, and permutations as well as include detailed calculations and solutions.

Answer the following Questions:

1. In some countries, phone numbers consist of an area code made up of two digits, and a local number made up of seven digits. Below are the requirements for 9 digit number:

           -The area code can be made up of any digit other than 9

           -The first digit of the local number cannot be 0

Given the requirements above; how many possible phone number combinations can these countries have?

2. How many ways are there to select three candidates from eight equally qualified recent graduates for openings in an accounting firm?

3. Ten prominent citizens have been nominated for a community’s “Citizen of the Year” award. First and second place trophies are awarded to the persons receiving the highest and second highest number of votes. In how many different ways can the trophies be awarded?

Explanation / Answer

(1)

Total number of area codes possible are = 9C1 * 9C1 = 81

Total number of local numbers possible are = 9C1 * 10C1 * 10C1 * 10C1 * 10C1 * 10C1 * 10C1 = 9 *10^7

Hence total number of phone number combinations are = 81 * 9 * 10^7 = 9^3 * 10^7 = 7290000000

(2)

3 candidates from 8 qualified graduates can be selected in 8C3 ways = 56

(3)

out of 10 prominent citizens any two can be selected for the awards.'

Hence selection can be done in 10C2 = 45 ways

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