   Chapter 9.7, Problem 5ES ### 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
2 views

# Use Theorem 9.5.1 to prove algebraically that ( r n ) = ( n − r n ) , for integers, n and r with 0 ≤ r ≤ n . (This can be done by direct calculation; it is not necessary to use mathematical induction.)

To determine

Use the formula (nr)=n!r!(nr)! to prove algebraically that (nr)=(n nr) for integers n and r with 0rn.

Explanation

Calculation:

Let us consider the theorem (nr)=n!r!(nr)!.

Now (nr)=n!r!(nr)! can be further simplified as shown below.

( n r )=n!( nr)!r! =n!( nr)![n( nr

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