**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? - [ ] ways2. How many ways are there to make a committee of ten board members if exactly three must be female? - [ ] ways3. 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.

Ways to make a committee of ten board members = 30C10=30!20!×10!=30045015

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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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

**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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