/*! 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} Q. 1.17 Present a combinatorial explanat... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q. 1.17 (page 19)

Present a combinatorial explanation of why

nr=nr,n-r

Short Answer

Expert verified

It is proved thatnr=nr,n-r

Step by step solution

01

Step 1. Given information.

It is given thatnr=nr,n-r.

02

Step 2. Give explanation for nr=nr, n-r

nrrepresents the no. of ways in which robjects can be selected from nobjects.

When this is done, robjects that are selected are grouped separately and n-robjects that are not selected are grouped separately.

Hence, this is equivalent to separating nobjects into two groups, one having robjects and another having n-robjects.

This can be done inn!r!(n-r)!ways=nr,n-r

Therefore,nr=nr,n-r.

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

Determine the number of vectors (x1,...,xn)such that each xiis a nonnegative integer and localid="1648403251141" 鈭�i=1nxi鈮�k

Prove the generalized version of the basic counting principle.

A total of nstudents are enrolled in a review course for the actuarial examination in probability. The posted

results of the examination will list the names of those who passed, in decreasing order of their scores. For instance, the posted result will be 鈥淏rown, Cho鈥� if Brown and Cho are the only ones to pass, with Brown receiving the higher score. Assuming that all scores are distinct (no ties), how many posted results are possible?

How many 5-digit numbers can be formed from the integers 1,2,...,9if no digit can appear more than twice? (For instance, 41434is not allowed.)

A well-known nursery rhyme starts as follows: 鈥淎s I was going to St. Ives I met a man with 7 wives. Each wife had 7 sacks. Each sack had 7 cats. Each cat had 7 kittens...鈥� How many kittens did the traveler meet

?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

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.