# DISCUSS ■ DISCOVER: Why Is ( n r ) the Same as C ( n , r ) ? This exercise explains why the binomial coefficients ( n r ) that appear in the expression of ( x + y ) n are the same as C ( n , r ) , the number of ways of choosing r objects from n objects. First, note that expanding a binomial using only the Distributive Property gives ( x + y ) 2 = ( x + y ) ( x + y ) = ( x + y ) x + ( x + y ) y = x x + x y + y x + y y ( x + y ) 3 = ( x + y ) ( x x + x y + y x + y y ) = x x x + x x y + x y x + x y y + y x x + y x y + y y x + y y y (a) Expand ( x + y ) 5 using only the Distribution Property. (b) Write all the terms that represent x 2 y 3 . These are all the terms that contain two x ’s and three y ’s. (c) Note that the two x ’s appear in all possible positions. Conclude that the number of terms that represent x 2 y 3 is C ( 5 , 2 ) . (d) In general, explain why ( n r ) in the Binomial Theorem is the same as C ( n , r ) .

### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
Publisher: Cengage Learning
ISBN: 9781305071742

### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
Publisher: Cengage Learning
ISBN: 9781305071742

#### Solutions

Chapter
Section
Chapter 14.1, Problem 94E
Textbook Problem

## Expert Solution

### Want to see the full answer?

Check out a sample textbook solution.See solution

### Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

See Solution

*Response times vary by subject and question complexity. Median response time is 34 minutes and may be longer for new subjects.