What Binomial coefficient is
The binomial coefficient is a number that represents the number of different ways that a set of items can be selected or arranged. It is also known as the “n choose k” coefficient and is usually represented by the notation:
n ( ) = k
The binomial coefficient represents the number of possibilities of selecting k objects from a set of n objects without regard to the order in which they were selected.
Steps for calculating the binomial coefficient:
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Determine the number of objects in the set, n.
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Determine the number of objects to be selected from the set, k.
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Calculate the binomial coefficient using the formula:
n ( ) = k
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Simplify the expression by factoring out common factors from the numerator and denominator.
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If possible, use the formula:
n! ( ) = k!(n − k)!
to calculate the binomial coefficient.
Examples
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Binomial coefficients are used when calculating the probability of a specific outcome in a Bernoulli trial, where there are two possible outcomes (e.g. success/failure).
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Binomial coefficients are used to calculate the number of combinations of a set of objects in which r objects are chosen from n objects.
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Binomial coefficients are used to calculate the probability of r successes in n trials when the probability of success is p.