There are ten female board members and twenty male board members. How many ways are there to make a committee of ten board members? ways How many ways are there to make a committee of ten board members if exactly three must be female? ways Determine the probability of selecting a committee of ten board members where exactly three of the members were female. Write your answer as a decimal, rounded to the nearest thousandth. Answer:
There are ten female board members and twenty male board members. How many ways are there to make a committee of ten board members? ways How many ways are there to make a committee of ten board members if exactly three must be female? ways Determine the probability of selecting a committee of ten board members where exactly three of the members were female. Write your answer as a decimal, rounded to the nearest thousandth. Answer:
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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![**Educational Website Content: Combinatorics and Probability**
**Problem Statement:**
There are ten female board members and twenty male board members.
1. How many ways are there to make a committee of ten board members?
- [ ] ways
2. How many ways are there to make a committee of ten board members if exactly three must be female?
- [ ] ways
3. Determine the *probability* of selecting a committee of ten board members where exactly three of the members were female. Write your answer as a decimal, rounded to the nearest thousandth.
- Answer: [ ]
**Explanation:**
This problem involves calculating the number of combinations in selecting a committee and finding the probability of a specific configuration.
- **Total Ways to Select Committee:** Here, you'll calculate from a pool of 30 total members (10 females + 20 males).
- **Ways to Select with Conditions:** Specify the number of combinations ensuring exactly three are female.
- **Probability Calculation:** Use the ratio of the favorable outcomes (from condition 2) to the total outcomes (condition 1) to find this probability.
For computations, consider using the combination formula:
\[ C(n, r) = \frac{n!}{r!(n-r)!} \]
where \( n \) is the total number of items to choose from, and \( r \) is the number of items to choose.
**Instructions:**
- Fill in the blanks by calculating the appropriate values using the combination formula.
- Ensure your final probability answer is a decimal rounded to the nearest thousandth.
This exercise helps solidify understanding of basic combinatorics and introduces probability-based event calculation in a practical scenario.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb788abcd-eef5-4f27-84e3-02815d880ffa%2Faabf0ef3-db38-4115-a18e-6a451bfadff0%2Fyko00k6_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Website Content: Combinatorics and Probability**
**Problem Statement:**
There are ten female board members and twenty male board members.
1. How many ways are there to make a committee of ten board members?
- [ ] ways
2. How many ways are there to make a committee of ten board members if exactly three must be female?
- [ ] ways
3. Determine the *probability* of selecting a committee of ten board members where exactly three of the members were female. Write your answer as a decimal, rounded to the nearest thousandth.
- Answer: [ ]
**Explanation:**
This problem involves calculating the number of combinations in selecting a committee and finding the probability of a specific configuration.
- **Total Ways to Select Committee:** Here, you'll calculate from a pool of 30 total members (10 females + 20 males).
- **Ways to Select with Conditions:** Specify the number of combinations ensuring exactly three are female.
- **Probability Calculation:** Use the ratio of the favorable outcomes (from condition 2) to the total outcomes (condition 1) to find this probability.
For computations, consider using the combination formula:
\[ C(n, r) = \frac{n!}{r!(n-r)!} \]
where \( n \) is the total number of items to choose from, and \( r \) is the number of items to choose.
**Instructions:**
- Fill in the blanks by calculating the appropriate values using the combination formula.
- Ensure your final probability answer is a decimal rounded to the nearest thousandth.
This exercise helps solidify understanding of basic combinatorics and introduces probability-based event calculation in a practical scenario.
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