Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
4. How many triangles can you draw using the dots below as vertices? a. Find an expression for the answer which is the sum of three terms involving binomial coefficients. b. Find an expression for the answer which is the difference of two binomial coefficients. c. Generalize the above to state and prove a binomial identity using a combinatorial proof. Say you have x points on the horizontal axis and y points in the semi-circle. Hint. There will be 185 triangles. But to find them... a. How many vertices of the triangle can be on the horizontal axis? b. Will any three dots work as the vertices?

4. How many triangles can you draw using the dots below as vertices? a. Find an expression for the answer which is the sum of three terms involving binomial coefficients. b. Find an expression for the answer which is the difference of two binomial coefficients. c. Generalize the above to state and prove a binomial identity using a combinatorial proof. Say you have x points on the horizontal axis and y points in the semi-circle. Hint. There will be 185 triangles. But to find them... a. How many vertices of the triangle can be on the horizontal axis? b. Will any three dots work as the vertices?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
4. How many triangles can you draw using the dots below as vertices? a. Find an expression for the answer which is the sum of three terms involving binomial coefficients. b. Find an expression for the answer which is the difference of two binomial coefficients. c. Generalize the above to state and prove a binomial identity using a combinatorial proof. Say you have x points on the horizontal axis and y points in the semi-circle. Hint. There will be 185 triangles. But to find them... a. How many vertices of the triangle can be on the horizontal axis? b. Will any three dots work as the vertices?
Transcribed Image Text:4. How many triangles can you draw using the dots below as vertices? a. Find an expression for the answer which is the sum of three terms involving binomial coefficients. b. Find an expression for the answer which is the difference of two binomial coefficients. c. Generalize the above to state and prove a binomial identity using a combinatorial proof. Say you have x points on the horizontal axis and y points in the semi-circle. Hint. There will be 185 triangles. But to find them... a. How many vertices of the triangle can be on the horizontal axis? b. Will any three dots work as the vertices?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 1 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS