| Definition: The binomial coefficient \left( {\begin{array}{*{20}{c}} n \\ k \\ \end{array}} \right) is read "n choose k". The formula for calculating: \left( {\begin{array}{*{20}{c}} n \\ k \\ \end{array}} \right) = \frac{{n!}}{{k!\left( {n - k} \right)!}} More
It is the coefficient of x^k in the polynomial expansion of the binomial power (1+x)^n , where n>k .
In combinatorics (probability and statistics), \left( {\begin{array}{*{20}{c}} n \\ k \\ \end{array}} \right) is interpreted as the number of k-element subsets (the k-combinations) of an n-element set, that is the number of ways that k things can be 'chosen' from a set of n things.
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GeoGebra Syntax: BinomialCoefficient[ <Number n>, <Number k> ]
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| Binomial Distribution - Application of GeoGebra command BinomialCoefficient
The theoretical probability of getting k successes in n trials with a probability p of success in any individual trial is: \left( {\begin{array}{*{20}{c}} n \\ k \\\end{array}} \right){p^k}{\left( {1 - p} \right)^{n - k}}
The binomial distribution of n trials with a probability p of success in any individual trial is the list of points:
BinDist =
Click on the Sequence[(k, BinomialCoefficient[n, k] p^k q^(n - k)), k, 0, n]
 to see the Binomial Distribution change with the number of trials n.
Click and drag the probability p of success to see the mean and skewness change.
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