Jse a tree diagram to find the number of ways 3 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 3 at a time. Does this answer differ from that in part (a) or (b)? a. If repetition is allowed, how many ways can 3 letters are chosen from the set {P,Q,R} if order is important? 27 o. If no repeats are allowed, how many ways can 3 letters are chosen from the set {P,Q,R} if order is important? c. Find the number of combinations of 3 elements taken 3 at a time.
Jse a tree diagram to find the number of ways 3 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 3 at a time. Does this answer differ from that in part (a) or (b)? a. If repetition is allowed, how many ways can 3 letters are chosen from the set {P,Q,R} if order is important? 27 o. If no repeats are allowed, how many ways can 3 letters are chosen from the set {P,Q,R} if order is important? c. Find the number of combinations of 3 elements taken 3 at a time.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![### Counting Methods
Use a tree diagram to find the number of ways 3 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 3 at a time. Does this answer differ from that in part (a) or (b)?**
---
#### a. If repetition is allowed, how many ways can 3 letters be chosen from the set {P, Q, R} if order is important?
![27]
#### Explanation:
The tree diagram shows that each letter can be repeated in each of the 3 positions, leading to \(3 \times 3 \times 3 = 27\) ways.
---
#### b. If no repeats are allowed, how many ways can 3 letters be chosen from the set {P, Q, R} if order is important?
![6]
#### Explanation:
No repetition means that once a letter is chosen, it cannot be reused. This gives us \(3 \times 2 \times 1 = 6\) ways.
---
#### c. Find the number of combinations of 3 elements taken 3 at a time.
![1]
#### Explanation:
In this case, combination means order does not matter. Since we are choosing all 3 letters out of 3, there is only 1 way: {P, Q, R}.
---
#### Does this answer differ from that in part (a) or (b)?
![Does this answer differ from that in part (a) or (b)?]
- ✅ **A. This answer differs from that in both parts (a) and (b).**
- ⬜ **B. This answer does not differ from that in parts (a) or (b).**
- ⬜ **C. This answer differs from that in part (b), but is the same as in part (a).**
- ⬜ **D. This answer differs from that in part (a), but is the same as in part (b).**
The correct answer is **A. This answer differs from that in both parts (a) and (b).**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb81a1ef6-0347-4062-b7ea-9e507390b385%2Fc8c123bb-b92a-43c5-9add-403b7c159436%2Fxmg3qf9_processed.png&w=3840&q=75)
Transcribed Image Text:### Counting Methods
Use a tree diagram to find the number of ways 3 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 3 at a time. Does this answer differ from that in part (a) or (b)?**
---
#### a. If repetition is allowed, how many ways can 3 letters be chosen from the set {P, Q, R} if order is important?
![27]
#### Explanation:
The tree diagram shows that each letter can be repeated in each of the 3 positions, leading to \(3 \times 3 \times 3 = 27\) ways.
---
#### b. If no repeats are allowed, how many ways can 3 letters be chosen from the set {P, Q, R} if order is important?
![6]
#### Explanation:
No repetition means that once a letter is chosen, it cannot be reused. This gives us \(3 \times 2 \times 1 = 6\) ways.
---
#### c. Find the number of combinations of 3 elements taken 3 at a time.
![1]
#### Explanation:
In this case, combination means order does not matter. Since we are choosing all 3 letters out of 3, there is only 1 way: {P, Q, R}.
---
#### Does this answer differ from that in part (a) or (b)?
![Does this answer differ from that in part (a) or (b)?]
- ✅ **A. This answer differs from that in both parts (a) and (b).**
- ⬜ **B. This answer does not differ from that in parts (a) or (b).**
- ⬜ **C. This answer differs from that in part (b), but is the same as in part (a).**
- ⬜ **D. This answer differs from that in part (a), but is the same as in part (b).**
The correct answer is **A. This answer differs from that in both parts (a) and (b).**
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