# Solve the Equations, Permutations and Combinations

1. As a business owner, there are many decisions that you need to make on a daily basis, such as ensuring you reach the highest production levels possible with your company's products. Your company produces two models of bicycles: Model A and Model B.

* Model A takes 2 hours to assemble.

* Model B takes 3 hours to assemble.

* Model A costs $25 to make per bike.

* Model B costs $30 to make per bike.

If your company has a total of 34 hours and $350 available per day for these two models, how many of each model can be made in a day?

Solve the equations for the different bicycle models that can be made daily with the any of the techniques - graphing, substitution, elimination, and matrix. How do you check your solution for both equations.

2. What are the differences between permutations and combinations? Give a real-world example of how permutations and combinations can be used and the details of the example in paragraph form. Which topics would be most applicable in your personal or professional life? Give specific examples.

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#### Solution Preview

Please see the attached file.

As a business owner, there are many decisions that you need to make on a daily basis, such as ensuring you reach the highest production levels possible with your company's products. Your company produces two models of bicycles: Model A and Model B.

Model A takes 2 hours to assemble.

Model B takes 3 hours to assemble.

Model A costs $25 to make per bike.

Model B costs $30 to make per bike.

If your company has a total of 34 hours and $350 available per day for these two models, how many of each model can be made in a day?

Solve the equations for the different bicycle models that can be made daily with the desired technique learned (graphing, substitution, elimination, and matrix).

Explain how to check your solution for both equations

Let x bikes of Model A and y bikes of ...

#### Solution Summary

Elimination method Used for Qn 1. and examples for permutations and combinations provided.

Fundamental Counting Principles: Permutation & Combination

1.) A club with 10 members is to pick a president, vice president, treasurer, and secretary. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?

2.) Find the value of the following expression:

a. 12P4

b. 12C4

c. 4P4

d. 10P8

e. 10C8

3.) A test has 10 true/false questions. How many different tests can be turned in to the teacher?

4.) A car is available in three types of models and in three types of colors. In how many combination can you buy the car?

5.) In how many ways can you make a four letter password from A, B, C, D and E if you are not allowed to repeat characters?

6.) In how many ways can you choose 7 cards from a deck of 52 cards?

7.) Use the fundamental counting principle to solve:

How many different four-letter radio stations call letters can be formed if the first letter must be W or K?

8.) Use the formula for C to solve:

A four person committee is to be elected from an organization's membership of 11 people. How many different committees are possible?

Please see the attached document for questions.

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