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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 nth power. So for n equals to three, the expansion is (a+b) × (a+b) × (a+b) which equals (a2+2ab+b2) × (a+b) which equals (a3 + 3ab2 + 3ba2 + b3). The coefficients are 1,3,3,1. These are listed in the third row of Pascal's triangle.


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