9. A bag contains 50 pennies, 50 nickels, 50 dimes and 50 quarters. You reach in and grab 30 coins. How many different outcomes are possible?
9. A bag contains 50 pennies, 50 nickels, 50 dimes and 50 quarters. You reach in and grab 30 coins. How many different outcomes are possible?
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...
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![**Problem 9:**
A bag contains 50 pennies, 50 nickels, 50 dimes, and 50 quarters. You reach in and grab 30 coins. How many different outcomes are possible?
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This problem involves calculating the number of combinations of coins that can be drawn from the bag, taking into account the different types of coins available. It requires an understanding of combinatorics, particularly the concept of combinations and permutations in probability.
This type of question is common in probability exercises, where you calculate the number of ways to choose items (in this case, coins) from a larger set. It challenges the student’s ability to use factorial notation and the combination formula:
\[ C(n, k) = \frac{n!}{k!(n-k)!} \]
Where:
- \( n \) is the total number of items to choose from,
- \( k \) is the number of items to choose,
- \( C(n, k) \) is the number of combinations.
Students would need to consider all possible distributions of coin types totaling 30 coins from the pool of 200 coins (50 of each type), considering the repetitions possible due to unlimited supply.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39ee8330-8a26-4cdb-b3ef-e7a0164aa18c%2Fa7a70bc4-deb1-4891-902c-563ce06b0878%2Fslxcxso_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 9:**
A bag contains 50 pennies, 50 nickels, 50 dimes, and 50 quarters. You reach in and grab 30 coins. How many different outcomes are possible?
---
This problem involves calculating the number of combinations of coins that can be drawn from the bag, taking into account the different types of coins available. It requires an understanding of combinatorics, particularly the concept of combinations and permutations in probability.
This type of question is common in probability exercises, where you calculate the number of ways to choose items (in this case, coins) from a larger set. It challenges the student’s ability to use factorial notation and the combination formula:
\[ C(n, k) = \frac{n!}{k!(n-k)!} \]
Where:
- \( n \) is the total number of items to choose from,
- \( k \) is the number of items to choose,
- \( C(n, k) \) is the number of combinations.
Students would need to consider all possible distributions of coin types totaling 30 coins from the pool of 200 coins (50 of each type), considering the repetitions possible due to unlimited supply.
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