1. Martha has 4 different colored pens in her bag. After she uses a pen she just throws it back into bag. If she does this 5 days a week, how many different ways can she use the pens for the week? a. 20 b. 3125 c. 256 d. 200 e. 1024
1. Martha has 4 different colored pens in her bag. After she uses a pen she just throws it back into bag. If she does this 5 days a week, how many different ways can she use the pens for the week? a. 20 b. 3125 c. 256 d. 200 e. 1024
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
![**Problem:**
Martha has 4 different colored pens in her bag. After she uses a pen, she just throws it back into the bag. If she does this 5 days a week, how many different ways can she use the pens for the week?
a. 20
b. 3125
c. 256
d. 200
e. 1024
**Explanation:**
Since Martha throws each pen back into the bag after use, each day's choice of pen does not affect the others. There are 4 choices of pens each day and she uses a pen for 5 days, making it a question of calculating the number of combinations with replacement.
This means that for each day she has 4 independent choices, leading to a total of \(4^5\) different combinations.
Calculate \(4^5\):
\[4 \times 4 \times 4 \times 4 \times 4 = 1024\]
Therefore, the correct answer is:
e. 1024](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F82664aa5-57b9-4a20-9cfb-d7df7435967c%2F8a7ddac9-6501-4d9e-8811-80a4ba7ab262%2F17bfe4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
Martha has 4 different colored pens in her bag. After she uses a pen, she just throws it back into the bag. If she does this 5 days a week, how many different ways can she use the pens for the week?
a. 20
b. 3125
c. 256
d. 200
e. 1024
**Explanation:**
Since Martha throws each pen back into the bag after use, each day's choice of pen does not affect the others. There are 4 choices of pens each day and she uses a pen for 5 days, making it a question of calculating the number of combinations with replacement.
This means that for each day she has 4 independent choices, leading to a total of \(4^5\) different combinations.
Calculate \(4^5\):
\[4 \times 4 \times 4 \times 4 \times 4 = 1024\]
Therefore, the correct answer is:
e. 1024
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON