Use a tree diagram to find the number of ways 2 letters can be chosen from the set (P,Q,R} if order is important and (a) if repetition is allowed; (b) if no repeats are allowed; (c) Find the number of combinations of 3 elements taken 2 at a time. Does this answer differ from that in part (a) or (b)? (a) If repetition is allowed, how many ways can 2 letters be chosen from the set {P,Q,R} if order is important? Choose the correct formula below, and if necessary, fill the answer boxes to complete your choice. (Type the terms of your expression in the same order as they appear in the original expression.) OA. M= OB. 3P₂= OC. 3C₂ = 3 3! (3-2) 2
Use a tree diagram to find the number of ways 2 letters can be chosen from the set (P,Q,R} if order is important and (a) if repetition is allowed; (b) if no repeats are allowed; (c) Find the number of combinations of 3 elements taken 2 at a time. Does this answer differ from that in part (a) or (b)? (a) If repetition is allowed, how many ways can 2 letters be chosen from the set {P,Q,R} if order is important? Choose the correct formula below, and if necessary, fill the answer boxes to complete your choice. (Type the terms of your expression in the same order as they appear in the original expression.) OA. M= OB. 3P₂= OC. 3C₂ = 3 3! (3-2) 2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Title: Understanding Combinations and Permutations Using a Tree Diagram**
**Introduction:**
Explore how to determine the number of ways to select 2 letters from the set {P, Q, R} using a tree diagram. Understand the implications of repetition and order in permutations and combinations.
**Tasks:**
1. **Allowing Repetition:**
Determine the number of ways to choose 2 letters from the set {P, Q, R} when repetition is permitted.
2. **No Repetition Allowed:**
Determine the number of ways to select 2 letters from the same set without allowing repeats.
3. **Combinations:**
Calculate the number of combinations of 3 elements taken 2 at a time, and assess whether this result differs from parts (a) or (b).
---
**Exercise:**
*(a)* If repetition is allowed, how many ways can 2 letters be chosen from the set {P, Q, R} if order is important? Choose the correct formula below, and, if necessary, fill in the answer boxes to complete your choice. *(Type the terms of your expression in the same order as they appear in the original expression.)*
- **A.** \( M = \) [ ]
- **B.** \( ^3P_2 = \frac{3!}{(3-2)!} \)
\( = \frac{3!}{1!} \)
- **C.** \( ^3C_2 = \frac{3!}{(3-2)! \cdot 2!} \)
\( = \frac{3!}{1! \cdot 2!} \)
---
By using these exercises, you will enhance your understanding of the fundamental concepts of permutations and combinations and how the order and repetition impact the calculation of possibilities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc5a22111-764a-4819-b35c-03f0b719ed5a%2F613ab029-7bf0-4f60-8738-3dad0504d0e5%2Fgjxsjca_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Combinations and Permutations Using a Tree Diagram**
**Introduction:**
Explore how to determine the number of ways to select 2 letters from the set {P, Q, R} using a tree diagram. Understand the implications of repetition and order in permutations and combinations.
**Tasks:**
1. **Allowing Repetition:**
Determine the number of ways to choose 2 letters from the set {P, Q, R} when repetition is permitted.
2. **No Repetition Allowed:**
Determine the number of ways to select 2 letters from the same set without allowing repeats.
3. **Combinations:**
Calculate the number of combinations of 3 elements taken 2 at a time, and assess whether this result differs from parts (a) or (b).
---
**Exercise:**
*(a)* If repetition is allowed, how many ways can 2 letters be chosen from the set {P, Q, R} if order is important? Choose the correct formula below, and, if necessary, fill in the answer boxes to complete your choice. *(Type the terms of your expression in the same order as they appear in the original expression.)*
- **A.** \( M = \) [ ]
- **B.** \( ^3P_2 = \frac{3!}{(3-2)!} \)
\( = \frac{3!}{1!} \)
- **C.** \( ^3C_2 = \frac{3!}{(3-2)! \cdot 2!} \)
\( = \frac{3!}{1! \cdot 2!} \)
---
By using these exercises, you will enhance your understanding of the fundamental concepts of permutations and combinations and how the order and repetition impact the calculation of possibilities.
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