/*! 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 50 Baskin-Robbins offers 31 differe... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 50

Baskin-Robbins offers 31 different flavors of ice cream. One of its items is a bowl consisting of three scoops of ice cream, each a different flavor. How many such bowls are possible?

Short Answer

Expert verified
There are 4495 different possible bowls of ice cream.

Step by step solution

01

Identify the combination formula

The combination formula is used when the order of selection does not matter. In this case, we are interested in groupings of ice cream scoops, not the order they are scooped. Therefore, the combination formula applies. It is given by \(C(n, r) = \frac{n!}{r!(n-r)!}\), where 'n' is the total number of items, 'r' is the number of items to choose, 'n!' is the factorial of 'n', and 'r!' is the factorial of 'r'.
02

Substitute the values into the combination formula

In this case, we have 'n' as 31 (the total number of flavors) and 'r' as 3 (the number of scoops in each bowl). Substituting these values into the formula, the calculation becomes: \(C(31, 3) = \frac{31!}{3!(31-3)!}\).
03

Carry out the factorial and simplification

First, calculate the factorials in the denominator. We have '3!' which equals to 6, and '(31-3)!' which equals to '28!', which is very large value and we don't need to calculate it because it will cancel out. Substitute them into the equation we get: \(= \frac{31*30*29*28!}{3*2*1*28!}\). The '28!' will cancel out. After canceling out and performing the multiplication, you will get the answer.

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

As in Exercise 1, six performers are to present their comedy acts on a weekend evening at a comedy club. One of the performers insists on being the last stand-up comic of the evening. If this performer's request is granted, how many different ways are there to schedule the appearances?

Figure \(\mathbf{1 1 . 2}\) on page 689 shows that a tree diagram can be used to find the total number of outfits. Describe one advantage of using the Fundamental Counting Principle rather than a tree diagram.

Explain how to find the expected value for the number of girls for a family with two children. What is the expected value?

A student is planning a two-part trip. The first leg of the trip is from San Francisco to New York, and the second leg is from New York to Paris. From San Francisco to New York, travel options include airplane, train, or bus. From New York to Paris, the options are limited to airplane or ship. In how many ways can the two-part trip be made?

Evaluate each factorial expression. \(\frac{19 !}{11 !}\)
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

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.