Counting & Binomials
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π = included in formula booklet β’ π« = not in formula booklet
Track your progress:
Don't know
Working on it
Confident
π = included in formula booklet β’ π« = not in formula booklet
Pascal's Triangle and nCr
Factorials
Factorials are shortcut used to express decreasing products of integers such as
The definition is
Fractions of factorials as partial products
Binomial Coefficient nCr
The number of ways to choose r items from a set of n items can be expressed as (nrβ), nβCrβ or nCrβ. The number of combinations can be calculated using the formula
Pascal's Triangle
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 nCrβ. Its symmetry and simple construction make it a powerful tool for exploring combinatorial relationships and probability.
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Binomial Theorem
The expansion of (a+b)βΏ
The binomial theorem allows us expand expressions of the form (a+b)n:
or in summation form: