A pianist plans to play 5 pieces at a recital from her repertoire of 20 pieces, and is carefully considering which song to play first, second, etc. to create a good flow. How many different recital programs are possible? **Problem Statement:**A pianist plans to play 5 pieces at a recital from her repertoire of 20 pieces, and is carefully considering which song to play first, second, etc. to create a good flow. How many different recital programs are possible?**Solution Explanation:**To solve this problem, consider that the order in which the pieces are played matters. This situation involves permutations since you are arranging 5 pieces out of 20.**Permutations Formula:**The number of permutations of choosing $ r $ items from $ n $ items is given by the formula:\[P(n, r) = \frac{n!}{(n-r)!}\]**Application to the Problem:**- $ n = 20 $ (total pieces)- $ r = 5 $ (pieces to be played)Using the formula:\[P(20, 5) = \frac{20!}{(20-5)!} = \frac{20!}{15!}\]Calculating this gives:\[= 20 \times 19 \times 18 \times 17 \times 16\]\[= 1,860,480\]Therefore, there are **1,860,480** different possible recital programs.

Given: Total number of pieces n = 20 Number of pieces a pianist plans to play r = 5 Formula Used:…

A pianist plans to play 5 pieces at a recital from her repertoire of 20 pieces, and is carefully considering which song to play first, second, etc. to create a good flow. How many different recital programs are possible?

A pianist plans to play 5 pieces at a recital from her repertoire of 20 pieces, and is carefully considering which song to play first, second, etc. to create a good flow. How many different recital programs are possible?

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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