/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 47 Nine bands have volunteered to p... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

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 total number of lineups possible for five bands, selected from nine, is 15120.

Step by step solution

01

Identify the total number of elements

In this problem, there are nine bands in total, so the total number of elements is nine.
02

Identify the number of elements to select

According to the information, only five bands can play. Therefore, we want to select five elements out of nine.
03

Calculate the permutation

This is a permutation problem since the order in which the bands perform is important. To get the number of lineups possible, we calculate the permutation, which can be done by using the formula \( P(n, k) = n! / (n-k)!\). Where n is the total number of elements (in this case, the total number of bands is 9), k is the number of elements to select (here, it's 5). So the calculation will be as follows: \( P(9, 5) = 9! / (9-5)! = 9! / 4! = 15120\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

You need to arrange ten of your favorite photographs on the mantel above a fireplace. How many ways can you arrange the photographs, assuming that the order of the pictures makes a difference to you?

A pizza can be ordered with three choices of size (small, medium, or large), four choices of crust (thin, thick, crispy, or regular), and six choices of toppings (ground beef, sausage, pepperoni, bacon, mushrooms, or onions). How many onetopping pizzas can be ordered?

Evaluate each factorial expression. \(\frac{106 !}{104 !}\)

Evaluate each factorial expression. \(\frac{700 !}{699 !}\)

The local seven-digit telephone numbers in Inverness, California, have 669 as the first three digits. How many different telephone numhers are possihle in Inverness?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.