Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Q. 1.14 (page 20)

Determine the number of vectors (x1,...,xn)such that each xiis a positive integer and

role="math" localid="1649161391681" ∑i=1nxi≤k

wherek≥n.

Short Answer

Expert verified

The no. of vectors are∑j=nkj-1n-1.

Step by step solution

01

Step 1. Given information.

It is given that ∑i=1nxi≤k

andk≥n.

02

Step 2. Find the no. of vectors.

There are j-1n-1positive vectors whose sum is j.

So, the possible no. of vectors are∑j=nkj-1n-1.

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

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

1. (a) How many different 7-place license plates are possible if the first 2 places are for letters and the other 5 for numbers? (b) Repeat part (a) under the assumption that no letter or number can be repeated in a single license plate

In a certain community, there are 3 families consisting of a single parent and 1 child, 3 families consisting of a single parent and 2 children, 5 families consisting of 2 parents and a single child, 7 families consisting of 2 parents and 2 children, and 6 families consisting of 2 parents and 3 children. If a parent and child from the same family are to be chosen, how many possible choices are there?

Delegates from 10countries, including Russia, France, England, and the United States, are to be seated in a row. How many different seating arrangements are possible if the French and English delegates are to be seated next to each other and the Russian and U.S. delegates are not to be next to each other?

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 “Brown, Cho” 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?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied 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.

Sign-up for free