# MATHEMATICS

MATH125: Unit 4 Submission Assignment Answer Form

Counting Techniques and Introduction to Probability

ALL questions below must be answered. Show ALL step-by-step calculation. Upload this modified Answer Form to the intellipath Unit 4 Submission lesson. Make sure you submit your work in a modified MS Word document; handwritten work will not be accepted. If you need assistance, please contact your course instructor.

Part A: Combinations & Permutations

1. Differentiate between permutations and combinations. How are they different? What is the formula for each? (15 points)

How are they different?

(5 pts)

?

Permutation Formula

(5 pts)

?

Combination Formula

(5 pts)

?

2. Each state has a standard format for license plates that includes a set number of alphanumeric characters. For this assignment, you can insert a picture of your state’s non-personalized license plate or provide a sample of the format in text. (20 points total for Question 2)

(1 pt)

?

(Or a Sample)

(1 pt)

?

(1 pt)

?

a. Determine the number of different license plates that can be created using this format. Assume that a license plate consists of seven alphanumeric characters using numbers (0-9) and capital letters (A-Z). Find how many unique license plates can be printed using all alphanumeric characters only once.

Is   this a permutation or combination? Why?

(2   pts)

?

What   formula from #1 above will you use to solve the problem?

(1   pt)

?

Solution:

(4   pts)

?

b. You and a friend are witnesses of a car accident in your state. But you can only remember a few of the first alphanumeric characters on the license plate.

How many alphanumeric characters do you   remember?

(1 pt)

?

(Select a number from 2 to 5)

What are the characters at the beginning?

(1 pt)

?

(4 pts)

?

How many license plates have been   eliminated?

(4 pts)

?

3. Your community has asked you to help the YMCA sports director organize a season of sports. You need to put together the teams. For the soccer teams, athletes signed up with three different age groups. How many different ways can you organize teams of ten for each age group? (15 points)

Are these a permutation or combination? Why?

(2 pt)

?

What formula from #1 above will you use   to solve the problem?

(1 pt)

?

How many students signed up for soccer?

(1 pt)

?

(Select a multiple of 10, from 30 to 100)

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