Theoretical introduction to βnβCrβ, or β(nrβ), and Pascal's triangle.
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Practice exam-style pascal's triangle and ncr problems
Factorials are shortcut used to express decreasing products of integers such as
The definition is
The number of ways to choose βrβ items from a set of βnβ items can be expressed as β(nrβ), βnβCrββ or βnCrβ. The number of combinations can be calculated using the formula
Pascal's triangle is a triangular array where each number is the sum of the two directly above it, beautifully revealing the coefficients of binomial expansions. Each term corresponds to a specific value of βnCrβ. Its symmetry and simple construction make it a powerful tool for exploring combinatorial relationships and probability.
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