   Chapter 9.6, Problem 6ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple are written in decreasing order but are not necessarily distinct? In other words, how many 5-tuples of integers ( h , i , j , k , m ) are there with n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1 ?

To determine

To find how many 5 tuples of integers (h,i,j,k,m) are there with nhijkm1.

Explanation

Given information:

Any quintuple (h,i,j,k,m), with nhijkm1 can be represented as a string of (n1) vertical bars and 5 crosses. The positions of the crosses indicate which 5 integers from 1 to n are indicated in the n tuple.

Concept used:

The number of r combinations with repetition allowed that can be selected from a set of n elements is (r+n1r).

Calculation:

Thus, the number of such quintuple is the same as the number of strings of (n1) vertical bars and 5 crosses.

i.e

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