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Chapter 11: Problem 47

Nine bands have volunteered to perform at a benefit concert, but there is only enough time for five of the bands to play. How many lineups are possible?

Short Answer

Expert verified
The number of possible lineups is 15120.

Step by step solution

01

Understanding The Problem

Firstly, one must understand the problem and note that this is a situation of permutation where order matters because the performances by bands are to occur one after the other, which makes the order of importance.
02

Identify The Formula

The formula for permutations of n items taken r at a time is given by \( nPr = \frac{n!}{(n-r)!} \)
03

Apply The Formula

Now, apply the formula for permutation. Here, n = 9 (the total number of bands) and r = 5 (the number of bands required to perform). So, the number of ways is given by \( 9P5 = \frac{9!}{(9-5)!} \)
04

Calculate The Number of ways

By calculating the factorials and making the division gives the total possible lineups = 15120

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