Problem 47
Question
Use the formula for \(_{n} P_{r}\) to solve Exercises \(41-48\) 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?
Step-by-Step Solution
Verified Answer
The total number of possible lineups is 15,120.
1Step 1: Understand the Concept
Understand that we are dealing with a Permutation problem. In Permutation order matters and here order of band playing matters.
2Step 2: Define the Variables for Permutation Formula
We need to define the variables that we know and calculate the corresponding factorials. Here, total number of bands \(n = 9\) and bands to be selected \(r = 5\).
3Step 3: Apply the Permutation Formula
The formula is \(_{n} P_{r} = \frac{n!}{(n-r)!}\). Substitute \(n = 9\) and \(r = 5\) in the formula.
4Step 4: Calculate the Factorials
Calculate the factorials in the formula.
5Step 5: Calculation
The final calculation step where we perform the division of the two factorials calculated in the previous step.
Other exercises in this chapter
Problem 46
Express each repeating decimal as a fraction in lowest terms. $$0 . \overline{1}=\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10,000}+\cdots$$
View solution Problem 46
Express each sum using summation notation. Use I as the lower limit of summation and i for the index of summation. $$5+5^{2}+5^{3}+\dots+5^{12}$$
View solution Problem 47
Exercises \(46-48\) will help you prepare for the material covered in ehe next section. Each exercise involves observing a pattern in the expanded form of the b
View solution Problem 47
A single die is rolled twice. Find the probability of rolling a 2 the first time and a 3 the second time.
View solution