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)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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  1. 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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