A bag contains 22 marbles: 4 are red, 7 are green, and 11 are blue. You reach in and pull out a sample of 6 marbles. 1. In how many ways can this sample of 6 marbles be taken (how many different samples are there)? 2. In how many of these samples are all the marbles the same color? 3. In how many of these samples are there exactly two red and two green marbles? 4. In how many of these samples do at least two different colors appear?

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: Marble Sample Analysis**

A bag contains a total of 22 marbles, distributed as follows: 4 are red, 7 are green, and 11 are blue. From this collection, you reach in and pull out a sample of 6 marbles.

**Questions:**

1. **Total Number of Samples**: In how many ways can this sample of 6 marbles be taken? Calculate all possible different combinations.
   
   [Answer Box]

2. **Uniform Color Samples**: In how many of these samples are all the marbles the same color?

   [Answer Box]

3. **Specific Color Combination**: In how many of these samples are there exactly two red marbles and two green marbles?

   [Answer Box]

4. **Varied Color Samples**: In how many of these samples do at least two different colors appear?

   [Answer Box]
Transcribed Image Text:**Problem Statement: Marble Sample Analysis** A bag contains a total of 22 marbles, distributed as follows: 4 are red, 7 are green, and 11 are blue. From this collection, you reach in and pull out a sample of 6 marbles. **Questions:** 1. **Total Number of Samples**: In how many ways can this sample of 6 marbles be taken? Calculate all possible different combinations. [Answer Box] 2. **Uniform Color Samples**: In how many of these samples are all the marbles the same color? [Answer Box] 3. **Specific Color Combination**: In how many of these samples are there exactly two red marbles and two green marbles? [Answer Box] 4. **Varied Color Samples**: In how many of these samples do at least two different colors appear? [Answer Box]
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