Answers only please. **Permutations of Three Items from a Group of Six**To determine how many permutations of three items can be selected from a group of six, follow the steps below. This exercise will help you understand permutations and how to list them systematically.**Problem Statement**:How many permutations of three items can be selected from a group of six?**Instructions**:1. Use the letters A, B, C, D, E, and F to identify the items.2. List each of the permutations of items B, D, and F.3. Enter your answers as a comma-separated list.4. Enter three unspaced capital letters for each permutation.**Steps to Solve**:1. **Identify the number of items and the group size**: - Total items: 6 (A, B, C, D, E, F) - Number of items to select: 32. **Calculate the permutations**: - The formula for permutations of selecting $ r $ items from $ n $ items is: \[ P(n, r) = \frac{n!}{(n-r)!} \] - For this problem, $ n = 6 $ and $ r = 3 $: \[ P(6, 3) = \frac{6!}{(6-3)!} = \frac{6 \times 5 \times 4 \times 3!}{3!} = 6 \times 5 \times 4 = 120 \] - Thus, there are 120 permutations of choosing 3 items from a group of 6.3. **List permutations of B, D, and F**: - For three specific items (B, D, F), generate the permutations: \[ \text{BDF, BFD, DBF, DFB, FBD, FDB} \]These permutations are important in helping understand how arrangements are made in different scenarios, whether in mathematics, computer science, or organizing physical and digital objects.**Optional Show My Work Section**:- Use this section to detail the steps and reasoning you used to find the permutations.- This can help in gaining a better understanding, and may also earn bonus points.**Need Help?**:- Click the "Read it" button if you need further assistance or examples on how to solve

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Description: Answers only please. **Permutations of Three Items from a Group of Six**To determine how many permutations of three items can be selected from a group of six, follow the steps below. This exercise will help you understand permutations and how to list

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2. [-/2.5 Points] DETAILS ASWESBE9 4.E.003. MY NOTES How many permutations of three items can be selected from a group of six? Use the letters A, B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F. (Enter your answers as a comma-separated list. Enter three unspaced capital letters for each permutation.) Need Help? Read It O Show My Work (Optional) ? What steps or reasoning did you use? Your work may add bonus points towards your score. You can submit show my work an unlimited number of times. Uploaded File (10 file maximum) No Files to Display O Upload File

2. [-/2.5 Points] DETAILS ASWESBE9 4.E.003. MY NOTES How many permutations of three items can be selected from a group of six? Use the letters A, B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F. (Enter your answers as a comma-separated list. Enter three unspaced capital letters for each permutation.) Need Help? Read It O Show My Work (Optional) ? What steps or reasoning did you use? Your work may add bonus points towards your score. You can submit show my work an unlimited number of times. Uploaded File (10 file maximum) No Files to Display O Upload File

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Author:Amos Gilat

Publisher:Amos Gilat

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Question

Answers only please.

**Permutations of Three Items from a Group of Six**

To determine how many permutations of three items can be selected from a group of six, follow the steps below. This exercise will help you understand permutations and how to list them systematically.

**Problem Statement**:

How many permutations of three items can be selected from a group of six?

**Instructions**:

1. Use the letters A, B, C, D, E, and F to identify the items.
2. List each of the permutations of items B, D, and F.
3. Enter your answers as a comma-separated list.
4. Enter three unspaced capital letters for each permutation.

**Steps to Solve**:

1. **Identify the number of items and the group size**:
- Total items: 6 (A, B, C, D, E, F)
- Number of items to select: 3

2. **Calculate the permutations**:
- The formula for permutations of selecting $ r $ items from $ n $ items is:
\[
P(n, r) = \frac{n!}{(n-r)!}
\]
- For this problem, $ n = 6 $ and $ r = 3 $:
\[
P(6, 3) = \frac{6!}{(6-3)!} = \frac{6 \times 5 \times 4 \times 3!}{3!} = 6 \times 5 \times 4 = 120
\]
- Thus, there are 120 permutations of choosing 3 items from a group of 6.

3. **List permutations of B, D, and F**:
- For three specific items (B, D, F), generate the permutations:
\[
\text{BDF, BFD, DBF, DFB, FBD, FDB}
\]

These permutations are important in helping understand how arrangements are made in different scenarios, whether in mathematics, computer science, or organizing physical and digital objects.

**Optional Show My Work Section**:
- Use this section to detail the steps and reasoning you used to find the permutations.
- This can help in gaining a better understanding, and may also earn bonus points.

**Need Help?**:
- Click the "Read it" button if you need further assistance or examples on how to solve

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