Pascal’s Triangle - “Hockey-stick Pattern” The partial sums of any diagonal appear in the next diagonal. For example, the sum of the first three terms in the second diagonal is the third entry in the third diagonal: 1 + 3 + 6 = 10 And we know we can also write this as: 2C2 + 3C2 + 4C2 = 5C3. Find a combinatorial explanation of this particular identity by showing how you can break down all of the 5C3 combinations into the required components.

Pascal’s Triangle - “Hockey-stick Pattern” The partial sums of any diagonal appear in the next diagonal. For example, the sum of the first three terms in the second diagonal is the third entry in the third diagonal: 1 + 3 + 6 = 10 And we know we can also write this as: 2C2 + 3C2 + 4C2 = 5C3. Find a combinatorial explanation of this particular identity by showing how you can break down all of the 5C3 combinations into the required components.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Pascal’s Triangle - “Hockey-stick Pattern”

The partial sums of any diagonal appear in the next diagonal. For example, the sum of the first three terms in the second diagonal is the third entry in the third diagonal:

1 + 3 + 6 = 10

And we know we can also write this as: 2C2 + 3C2 + 4C2 = 5C3.

Find a combinatorial explanation of this particular identity by showing how you can break down all of the 5C3 combinations into the required components.

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