/*! 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 372 How many telephone numbers of fo... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 372

How many telephone numbers of four different digits each can be made from the digits \(0,1,2,3,4,5,6,7,8,9 ?\)

Short Answer

Expert verified
There are 4536 telephone numbers of four different digits each that can be made from the given digits, considering that the numbers must be distinct and the first digit cannot be 0.

Step by step solution

01

Understanding Permutations

Permutations refer to the arrangement of objects in a specific order. In this case, we are arranging 4 digits out of the given 10 digits. Since we are choosing distinct digits, we can use the formula for permutations without repetition.
02

Apply the permutation formula

The formula for permutations without repetition is: \(P(n, r) = \frac{n!}{(n-r)!}\) Where: - n is the number of elements to choose from - r is the number of elements chosen - ! denotes the factorial (e.g., 5! = 5 脳 4 脳 3 脳 2 脳 1 = 120) Since we have 9 options for the first digit (1-9) and 9 remaining options for the second digit (0 and the remaining 8 digits not chosen in the first step), we need to calculate permutations in two stages: 1. Choosing the first digit (9 options) 2. Choosing the second, third, and fourth digits (9 options each)
03

Calculate the permutations for each stage

1. Permutations for choosing the first digit (from 1-9): \(P(9, 1) = \frac{9!}{(9-1)!} = \frac{9!}{8!} = 9\) 2. Permutations for choosing the second, third, and fourth digits (9 options): Since we have 9 options for each position, we can first calculate the permutation for three digits and then multiply by 9. \(P(9, 3) = \frac{9!}{(9-3)!} = \frac{9!}{6!} = 9 脳 8 脳 7\)
04

Multiply the permutations

Now, multiply the permutations from Step 3 to get the total number of unique 4-digit telephone numbers: Total permutations = Permutations for first digit 脳 Permutations for remaining digits Total permutations = 9 脳 9 脳 8 脳 7 = 4536 Hence, there are 4536 telephone numbers of four different digits each that can be made from the given digits.

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

Two ordinary dice are rolled. In how many different ways can they fall? How many of these ways will give a sum of nine?

How many permutations of two letters each can be formed from the letters \(\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}\) ? Actually write these permutations

Simplify the expression \([(5 !-4 !) / 6 !]\).

Find the expansion of \((\mathrm{x}+\mathrm{y})^{6}\).

Find the value of \(\mathrm{C}(\mathrm{n}, 0)\).
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Calculus

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.