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There are 10 women and 3 men signed up to join a salsa dance class. In how many ways can the Instructor choose 6 of the people to join if fewer than 2 must be men? 0 X S

There are 10 women and 3 men signed up to join a salsa dance class. In how many ways can the Instructor choose 6 of the people to join if fewer than 2 must be men? 0 X S

A First Course in Probability (10th Edition)
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 Statement:** There are 10 women and 3 men signed up to join a salsa dance class. In how many ways can the instructor choose 6 of the people to join if fewer than 2 must be men? **Explanation:** To solve this problem, we need to ensure that fewer than 2 men are chosen. This means we can either choose 0 men or 1 man. 1. **Choosing 0 men:** - All 6 members chosen are women. - The number of ways to choose 6 women from 10 is given by the combination formula \( C(n, k) \), where \( n \) is the total number, and \( k \) is the number of selections. - Thus, \( C(10, 6) \). 2. **Choosing 1 man:** - 5 members are women and 1 is a man. - The number of ways to choose 5 women from 10 is \( C(10, 5) \). - The number of ways to choose 1 man from 3 is \( C(3, 1) \). - Multiply these two combinations to find the total number of ways for this scenario. **Input Fields and Controls:** - There is an input field for entering your answer. - Buttons include: - A check button to verify your answer. - An option to reset the question. **Considerations for Solution:** Make sure to perform calculations for both scenarios (0 men, 1 man) and sum those possibilities to get the final total.
Transcribed Image Text:**Problem Statement:** There are 10 women and 3 men signed up to join a salsa dance class. In how many ways can the instructor choose 6 of the people to join if fewer than 2 must be men? **Explanation:** To solve this problem, we need to ensure that fewer than 2 men are chosen. This means we can either choose 0 men or 1 man. 1. **Choosing 0 men:** - All 6 members chosen are women. - The number of ways to choose 6 women from 10 is given by the combination formula \( C(n, k) \), where \( n \) is the total number, and \( k \) is the number of selections. - Thus, \( C(10, 6) \). 2. **Choosing 1 man:** - 5 members are women and 1 is a man. - The number of ways to choose 5 women from 10 is \( C(10, 5) \). - The number of ways to choose 1 man from 3 is \( C(3, 1) \). - Multiply these two combinations to find the total number of ways for this scenario. **Input Fields and Controls:** - There is an input field for entering your answer. - Buttons include: - A check button to verify your answer. - An option to reset the question. **Considerations for Solution:** Make sure to perform calculations for both scenarios (0 men, 1 man) and sum those possibilities to get the final total.
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