Factorial!

1. 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

4 * 3 * 2 * 1 = 24
This is called factorial.

Explanation

4 * 3 * 2 * 1 = 24
This is called factorial.

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

0

1

2

3

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.

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.

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

0

1

2

3

1 because there is only 1 student left.

Explanation

1 because there is only 1 student left.

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

9

6

3

2

1

All 6 different ways are shown above.

Explanation

All 6 different ways are shown above.

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

4

16

24

96

All 24 different ways are shown above.

Explanation

All 24 different ways are shown above.

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

Factor

Product

Factorial

Addend

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

Explanation

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

7. How many different possibilities are there for the first student?

1

2

3

4

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

Explanation

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

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

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.

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.

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

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

Explanation

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

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

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.

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.

11. 4! = 4 * 3 * 2 * 1 = 24
This is called factorial. The symbol for factorial is the exclamation point. 4! = 24
3! = 3 * 2 * 1 = 6, so 3! = 6
Mark 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

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

Explanation

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

Submit

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.

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.

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.

Submit