### Casting Combinatorics Exercise**Scenario:**There are 5 men and 8 women auditioning for the school play. Consider the following questions to understand how different combinations of the cast can be formed. **Questions:**1. **If the cast consists of 2 women *and* 2 men, how many different casts can be selected?** - **Explanation:** You need to calculate the number of ways to choose 2 women from 8 and 2 men from 5. This involves combinatorial calculations.2. **If the cast consists of 2 women *or* 2 men, how many different casts can be selected?** - **Explanation:** Determine the number of ways to select either 2 women from the 8 women or 2 men from the 5 men. This is an application of the addition rule in combinatorics.**Symbols for Input:**- For each question, you will input the number of possible combinations using a numerical input next to the question.### Note:This exercise is designed to help understand the basic principles of combinatorics, specifically focusing on selection and combination calculations.

Given : Number of men = 5 Number of women = 8

Answered: There are 5 men and 8 women auditioning…

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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There are 5 men and 8 women auditioning to be in the school play. Answer the following questions: 1. If the cast consists of 2 women and 2 men, how many different casts can be selected? 2. If the cast consists of 2 women or 2 men, how many different casts can be selected?