# Pascal's Triangle

## History, Binomial Numbers Or Coefficients, Pascal, Probability Theory

Pascal's triangle is a well-known set of numbers aligned in the shape of a **pyramid**. The numbers represent the binomial coefficients. Binomial coefficients represent the number of subsets of a given size. The numbers in Pascal's triangle are also the coefficients of the expansion of (a+b)^{n}, (a+b) raised to the n^{th} power. So for n equals to three, the expansion is (a+b) × (a+b) × (a+b) which equals (a^{2}+2ab+b^{2}) × (a+b) which equals (a^{3} + 3ab^{2} + 3ba^{2} + b^{3}). The coefficients are 1,3,3,1. These are listed in the third row of Pascal's triangle.

## Additional topics

- Pascal's Triangle - History
- Pascal's Triangle - Binomial Numbers Or Coefficients
- Pascal's Triangle - Pascal
- Pascal's Triangle - Probability Theory
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