Factorial!

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Which pattern of mathematical operations works for both 3 students, resulting in 6 ways, and also for 4 students, resulting in 24 ways?
- 4 + 3 + 2 + 1
- 4 * 3 * 2 * 1
- 4 + 3 * 2 * 1
- 4 + 3 + 2 * 1

About This Quiz

This is in preparation for writing a program to calculate the factorial of a user-provided number.

2.

After someone takes the first spot in the line, how many different possibilities are there for the second student?
- 0
- 1
- 2
- 3
Correct Answer

A. 2

Explanation

2 because if Abigail is first in line, then the 2nd student can be either Brent or Candy. Once a student is in the first spot, there are only 2 students left to choose from for the second spot.

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3.

After the first and second spots have been taken, how many students are available for the 3rd spot?
- 0
- 1
- 2
- 3
Correct Answer

A. 1

Explanation

1 because there is only 1 student left.

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4.

How many different orders can 3 students be in when they are standing in a line?
- 9
- 6
- 3
- 2
- 1
Correct Answer

A. 6

Explanation

All 6 different ways are shown above.

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5.

How many different arrangements can 4 students be in, when they are standing in a line?
- 4
- 16
- 24
- 96
Correct Answer

A. 24

Explanation

All 24 different ways are shown above.

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6.

In 4! = 2 * 3 * 4 = 24, what is 24 called more specifically than a product?
- Factor
- Product
- Factorial
- Addend
Correct Answer

A. Factorial

Explanation

In 4! = 2 * 3 * 4 = 24, the 24 is a specific kind of product called a factorial.

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7.

How many different possibilities are there for the first student?
- 1
- 2
- 3
- 4
Correct Answer

A. 3

Explanation

3 because the student could be Abigail, Brent, or Candy.

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8.

What can you do with the numbers 3, 2, and 1 to get the answer 6?
- 3 + 2 + 1 = 6
- 3 * 2 * 1 = 6
- 3 + 2 * 1 = 5
- Both A and B result in 6, but B is the correct one, 3 * 2 * 1 = 6
Correct Answer

A. Both A and B result in 6, but B is the correct one, 3 * 2 * 1 = 6

Explanation

The fundamental counting principal of probability tells us to multiply the numbers of ways for each spot. Let's look at another situation in which multiplication is the only one that will work.

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9.

Terms are multiplied. Numbers are multiplied. Multipliers are multiplied. Which of these is also a word for any numbers that are being multiplied?
- Factors
- Products
- Factorials
- Addends
Correct Answer

A. Factors

Explanation

In 4! = 2 * 3 * 4 = 24, the 2, 3, and 4 are called factors.

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10.

Which of these assignment statements could be used for accumulating a sum in a computer program?
- Sum = Number + Number + Number
- Sum = Sum + Number
- Sum = 0
- Sum = Addend
Correct Answer

A. Sum = Sum + Number

Explanation

Sum = Sum + Number is used for accumulating a sum. The value in memory has the new number added to it and the new sum replaces the old sum in memory.

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11.

4! = 4 * 3 * 2 * 1 = 24 This is called factorial. The symbol for factorial is the exclamation point. 4! = 243! = 3 * 2 * 1 = 6, so 3! = 6Mark ALL of the following that are acceptable ways to show how 4 factorial is equal to 24.
- 4! = 1 * 2 * 3 * 4 = 24
- 4! = 4 * 3 * 2 * 1 = 24
- 4! = 4 * 3 * 2 = 24
- 4! = 2 * 3 * 4 = 24
Correct Answer(s)

A. 4! = 1 * 2 * 3 * 4 = 24
A. 4! = 4 * 3 * 2 * 1 = 24
A. 4! = 4 * 3 * 2 = 24
A. 4! = 2 * 3 * 4 = 24

Explanation

All of these are acceptable ways to show that 4! = 24.

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12.

Sing the variables Factor and Factorial, extend your understanding of accumulating a sum to adapt it to calculating a factorial, one factor at a time. Write the assignment statement.

Correct Answer(s)
Factorial = Factorial * Factor
factorial = factorial * factor
Factorial=Factorial*Factor
factorial=factorial*factor
Factorial = Factor * Factorial

Explanation
You might have the concept correct but made a mispelling. I am not telling you the correct answer now though, because you will be putting this in your program.

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Current Version
Jan 11, 2013

Quiz Edited by
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Apr 26, 2010

Quiz Created by
Jhangen

Factorial!

Which pattern of mathematical operations works for both 3 students, resulting in 6 ways, and also for 4 students, resulting in 24 ways?

Quiz Preview

After someone takes the first spot in the line, how many different possibilities are there for the second student?

After the first and second spots have been taken, how many students are available for the 3rd spot?

How many different orders can 3 students be in when they are standing in a line?

How many different arrangements can 4 students be in, when they are standing in a line?

In 4! = 2 * 3 * 4 = 24, what is 24 called more specifically than a product?

How many different possibilities are there for the first student?

What can you do with the numbers 3, 2, and 1 to get the answer 6?

Terms are multiplied. Numbers are multiplied. Multipliers are multiplied. Which of these is also a word for any numbers that are being multiplied?

Which of these assignment statements could be used for accumulating a sum in a computer program?

4! = 4 * 3 * 2 * 1 = 24 This is called factorial. The symbol for factorial is the exclamation point. 4! = 243! = 3 * 2 * 1 = 6, so 3! = 6Mark ALL of the following that are acceptable ways to show how 4 factorial is equal to 24.

Sing the variables Factor and Factorial, extend your understanding of accumulating a sum to adapt it to calculating a factorial, one factor at a time. Write the assignment statement.