How many different committees can be formed from 12 teachers and 39 students if the committee consists of 3 teachers and 2 students? committees can be formed.
How many different committees can be formed from 12 teachers and 39 students if the committee consists of 3 teachers and 2 students? committees can be formed.
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:**
How many different committees can be formed from 12 teachers and 39 students if the committee consists of 3 teachers and 2 students?
**Solution Approach:**
To find the number of different committees, consider the following steps:
1. **Choose the Teachers:**
- We need to select 3 teachers from a group of 12. The number of ways to do this is given by the combination formula \(\binom{n}{r}\), which represents the number of ways to choose \(r\) items from \(n\) items without regard to order.
- Therefore, the number of ways to choose 3 teachers from 12 is \(\binom{12}{3}\).
2. **Choose the Students:**
- Similarly, we need to select 2 students from a group of 39.
- The number of ways to choose 2 students from 39 is \(\binom{39}{2}\).
3. **Calculate the Total Number of Committees:**
- Multiply the number of ways to choose the teachers by the number of ways to choose the students to find the total number of possible committees.
- Total committees = \(\binom{12}{3} \times \binom{39}{2}\).
**Input:**
- 12 teachers
- 39 students
**Output:**
- [ ] committees can be formed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4726056b-a0d8-4167-a534-8f03670a441a%2F61dea01b-b8f6-480b-b6ed-b8f6bd0fd479%2Fxewmqw_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
How many different committees can be formed from 12 teachers and 39 students if the committee consists of 3 teachers and 2 students?
**Solution Approach:**
To find the number of different committees, consider the following steps:
1. **Choose the Teachers:**
- We need to select 3 teachers from a group of 12. The number of ways to do this is given by the combination formula \(\binom{n}{r}\), which represents the number of ways to choose \(r\) items from \(n\) items without regard to order.
- Therefore, the number of ways to choose 3 teachers from 12 is \(\binom{12}{3}\).
2. **Choose the Students:**
- Similarly, we need to select 2 students from a group of 39.
- The number of ways to choose 2 students from 39 is \(\binom{39}{2}\).
3. **Calculate the Total Number of Committees:**
- Multiply the number of ways to choose the teachers by the number of ways to choose the students to find the total number of possible committees.
- Total committees = \(\binom{12}{3} \times \binom{39}{2}\).
**Input:**
- 12 teachers
- 39 students
**Output:**
- [ ] committees can be formed.
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