**Problem 5:**There are 19 boys and 13 girls in a Chemistry class. The teacher is randomly assigning students to lab groups of 4 students each. What is the probability that the first group selected will have only boys?---To solve this problem, you need to determine the probability of selecting 4 boys from the 19 available boys when mixed with the total students (19 boys + 13 girls = 32 students).First, calculate the total number of ways to choose any 4 students from the class:\[\binom{32}{4} = \frac{32 \times 31 \times 30 \times 29}{4 \times 3 \times 2 \times 1}\]Next, calculate the number of ways to choose 4 boys from the 19 boys:\[\binom{19}{4} = \frac{19 \times 18 \times 17 \times 16}{4 \times 3 \times 2 \times 1}\]Finally, the probability that the first group selected will have only boys is given by:\[\frac{\binom{19}{4}}{\binom{32}{4}}\]

The provided information are: Number of boys = 19 Number of girls = 13 Total number of students =…

5) There are 19 boys and 13 girls in a Chemistry class. The teacher is randomly assigning students to lab groups of 4 students each. What is the probability the first group selected will have only boys?

5) There are 19 boys and 13 girls in a Chemistry class. The teacher is randomly assigning students to lab groups of 4 students each. What is the probability the first group selected will have only boys?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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

**Problem 5:**
There are 19 boys and 13 girls in a Chemistry class. The teacher is randomly assigning students to lab groups of 4 students each. What is the probability that the first group selected will have only boys?

---

To solve this problem, you need to determine the probability of selecting 4 boys from the 19 available boys when mixed with the total students (19 boys + 13 girls = 32 students).

First, calculate the total number of ways to choose any 4 students from the class:
\[
\binom{32}{4} = \frac{32 \times 31 \times 30 \times 29}{4 \times 3 \times 2 \times 1}
\]

Next, calculate the number of ways to choose 4 boys from the 19 boys:
\[
\binom{19}{4} = \frac{19 \times 18 \times 17 \times 16}{4 \times 3 \times 2 \times 1}
\]

Finally, the probability that the first group selected will have only boys is given by:
\[
\frac{\binom{19}{4}}{\binom{32}{4}}
\]

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