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 (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.