/*! 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 56 To win in the New York State lot... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 56

To win in the New York State lottery, one must correctly select 6 numbers from 59 numbers. The order in which the selection is made does not matter. How many different selections are possible?

Short Answer

Expert verified
The total number of different selections possible is the value obtained in Step 4.

Step by step solution

01

Understanding Combinations

Combinations can be calculated using the formula for combinations which is \( C(n, k) = \frac{n!}{k!(n-k)!} \), where n is the total number of items, k is the number of items to choose, and '!' indicates factorial.
02

Applying the combinations formula

Given that there are 59 numbers (n=59) and we need to select 6 numbers (k=6), we can simply substitute these values into the combinations formula. So, the calculation would be \( C(59, 6) = \frac{59!}{6!(59-6)!} \).
03

Calculating Factorials

The factorial function can be computed as the product of all positive integers up to the designated number. \( 59! = 59*58*57*...*1 \), \( 6! = 6*5*4*3*2*1 \), and \( (59-6)! = 53*52*51*...*1 \). These values can be computed with a calculator.
04

Performing the Division

After calculating the factorials, divide the numerator by the denominator to get the total number of combinations.

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

For the first 30 days of a flu outbreak, the number of students on your campus who become ill is increasing. Which is worse: The number of students with the flu is increasing arithmetically or is increasing geometrically? Explain your answer.

Use the formula for the value of an annuity to solve Exercises 77鈥�84. Round answers to the nearest dollar. To offer scholarship funds to children of employees, a company invests \(\$ 15,000\) at the end of every three months in an annuity that pays \(9 \%\) compounded quarterly. a. How much will the company have in scholarship funds at the end of ten years? b. Find the interest.

You are dealt one card from a standard 52-card deck. Find the probability of being dealt $$\text{a diamond.}$$

Suppose that it is a drawing in which the Powerball jackpot is promised to exceed \(\$ 700\) million. If a person purchases \(292,201,338\) tickets at \(\$ 2\) per ticket (all possible combinations), isn't this a guarantee of winning the jackpot? Because the probability in this situation is \(1,\) what's wrong with doing this?

Mega Millions is a multi-state lottery played in most U.S. states. As of this writing, the top cash prize was \(\$ 656\) million, going to three lucky winners in three states. Players pick five different numbers from 1 to 56 and one number from 1 to \(46 .\) Use this information to solve Exercises \(27-30 .\) Express all probabilities as fractions. A player wins a minimum award of \(\$ 10,000\) by correctly matching four numbers drawn from white balls ( 1 through 56 ) and matching the number on the gold Mega Bali (1 through 46 ). What is the probability of winning this consolation prize?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

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.