A movie theater can play 30 westerns, 15 science fiction movies, and 10 horror movies (all movies are distinct from each other). Its standard daily program typically consists of a western followed by a science fiction movie, and then a horror movie. 1. How many different programs can it play? 2. How many different programs are there if the three movies can be played in any order? How does this number compare to the previous number and why? 3. How many different three-movie programs are there if there are absolutely no restrictions (e.g., the same movie can be played twice, movies can be played in any order, categories do not matter, etc.)? How does this number compare to the previous numbers and why?

A movie theater can play 30 westerns, 15 science fiction movies, and 10 horror movies (all movies are distinct from each other). Its standard daily program typically consists of a western followed by a science fiction movie, and then a horror movie. 1. How many different programs can it play? 2. How many different programs are there if the three movies can be played in any order? How does this number compare to the previous number and why? 3. How many different three-movie programs are there if there are absolutely no restrictions (e.g., the same movie can be played twice, movies can be played in any order, categories do not matter, etc.)? How does this number compare to the previous numbers and why?

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.CT: Chapter Test

Problem 2CT: A hospital cafeteria offers a fixed-price lunch consisting of a main course, a dessert, and a drink....

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