Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Q.1.28 (page 16)

If 8new teachers are to be divided among 4schools, how many divisions are possible? What if each school must receive 2teachers?

Short Answer

Expert verified

(a)65530-- the basic principle of counting

(b)2520- use the multinomials.

Step by step solution

01

Given Information.

Let 8new teachers are to be divided among 4schools.

02

Part (a) Explanation.

Divide 8people among 4schools

The teachers are different among themselves, and so are the schools.

Every teacher can choose a school. By the basic principle of counting:

localid="1649848745500" 4·4·4·4·4·4·4·4=48=65536different divisions of the teachers.

03

Part (b) Explanation.

Every school gets preciseness 2teachers:

To divide 8different objects into four groups of fixed sizes2,2,2and2.

localid="1649848759459" 82,2,2,2=8!2!2!2!2!=2520.different divisions of the teachers.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

How many vectors x1,...,xkare there for which each role="math" localid="1647853392605" xiis a positive integer such that role="math" localid="1647853435585" 1≤xi≤nandrole="math" localid="1647853511159" x1<x2<···<xk?

Argue that

nn1,n2,........,nr=n-1n1-1,n2,........,nr+n-1n1,n2-1,........,nr+......+n-1n1,n2,........,nr-1

Hint: Use an argument similar to the one used to establish Equation (4.1).

Ten weight lifters are competing in a team weight-lifting contest. The lifters 3are from the United States,4are from Russia, 2are from China, and 1are from Canada. If the scoring takes account of the countries that the lifters represent, but not their individual identities, how many different outcomes are possible from the point of view of scores? How many different outcomes correspond to results in which the United States has 1competitors in the top three and 2in the bottom three?

Give an analytic verification of

n2=k2+k(n-k)+n-k2,1≤k≤n

Now, give a combinatorial argument for this identity.

A student is to answer 7 out of 10 questions in an examination. How many choices has she? How many if she must answer at least 3 of the first 5 questions?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Probability and Statistics

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.

Sign-up for free