/*! 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 61 Solve by the method of your choi... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Solve by the method of your choice. From a club of 20 people, in how many ways can a group of three members be selected to attend a conference?

Short Answer

Expert verified
The group of three members can be selected in 1140 different ways.

Step by step solution

01

Identify values for \(n\) and \(k\)

In this problem, the total number of people, \(n\), is 20. The number of people to choose, \(k\), is 3.
02

Substitute the values into the formula

Substitute these values into the combination formula: \( C(n, k) = \dfrac{20!}{3!(20-3)!} \) = \( \dfrac{20!}{3! \cdot 17!} \)
03

Simplify the expression

First calculate the factorial for these numbers \(20!\), \(3!\) and \(17!\) . Then substitute the obtained values into the combination equation and simplify.
04

Simplify the equation

Simplify the equation to obtain 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 91Ó°ÊÓ!

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

Use the Fundamental Counting Principle to solve A restaurant offers the following lunch menu. $$ \begin{array}{llll} \text { Main Course } & \text { Vegetables } & \text { Beverages } & \text { Desserts } \\ \text { Ham } & \text { Potatoes } & \text { Coffee } & \text { Cake } \\ \text { Chicken } & \text { Peas } & \text { Tea } & \text { Pie } \\ \text { Fish } & \text { Green beans } & \text { Milk } & \text { Ice cream } \\\ \text { Beef } & & \text { Soda } & \end{array} $$ If one item is selected from each of the four groups, in how many ways can a meal be ordered? Describe two such orders.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Assuming the next U.S. president will be a Democrat or a Republican, the probability of a Republican president is 0.5.

Use the formula for \(_{n} C_{r}\) to solve Of the 100 people in the U.S. Senate, 18 serve on the Foreign Relations Committee. How many ways are there to select Senate members for this committee (assuming party affiliation is not a factor in selection)?

Exercises \(67-72\) are based on the following jokes about books: \(\cdot\) "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." - Groucho Marx \(\cdot\) "I recently bought a book of free verse. For \(\$ 12\)." \- George Carlin \(\cdot\) "If a word in the dictionary was misspelled, how would we know?" - Steven Wright \(\cdot\) "Encyclopedia is a Latin term. It means 'to paraphrase a term paper." - Greg Ray \(\cdot\) "A bookstore is one of the only pieces of evidence we have that people are still thinking." - Jerry Seinfeld \(\cdot\) "I honestly believe there is absolutely nothing like going to bed with a good book. Or a friend who's read one." \(-\)Phyllis Diller If the order in which these jokes are told makes a difference in terms of how they are received, how many ways can they be delivered if a joke by a man is told first?

A section in a stadium has 20 seats in the first row, 23 seats in the second row, increasing by 3 seats each row for a total of 38 rows. How many seats are in this section of the stadium?A section in a stadium has 20 seats in the first row, 23 seats in the second row, increasing by 3 seats each row for a total of 38 rows. How many seats are in this section of the stadium?

See all solutions

Recommended explanations on Math Textbooks

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.