Pascal and His Formulas

pascal triangle
The Pascal triangle (actually known long before Pascal) is a table of the binomial coefficients where the (n, k)th entry is .
Each entry is the sum of the pair immediately above it.
binomial coefficient
The binomial coefficients are the coefficients of powers of x in the expansion of (1 + x)n.
We have
where the binomial coefficient is the number of ways of choosing an (unordered) subset of size k from a set of size n.
The binomial coefficients are the entries in the Pascal triangle.
binomial theorem
The Binomial Theorem is the result which allows one to expand a binomial:
(x + y)n = xn + an-1xn-1y + an-2xn-2y2 + ... + yn
where the coefficients ai are called binomial coefficients
probability theory Probability theory studies the possible outcomes of given events together with their relative likelihoods and distributions.
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