The Binomial theorem gives the coefficients of the product of n equal binomials:
(x + b)n = (x + b)(x + b)• • • (x + b).
If we expanded
(x + b)4
for example, then before adding the like terms, we would find term in
x4, x3b, x²b², xb3, and b4.
A binomial coefficient equals the number of combinations of r items that can be selected from a set of n items. It also represents an entry in Pascal’s triangle. These numbers are called binomial coefficients because they are coefficients in the Binomial theorem.
What the binomial theorem does is tell how many terms there are of each kind -- it adds those like terms. Those are the binomial coefficients.
We will see that determining those coefficients depends on the theory of combinations.
Binomial coefficient is intimately related to Bernoulli numbers, Catalán numbers, Fibonacci numbers, statistics and a host of combinatoric problems.
(x + b)n = (x + b)(x + b)• • • (x + b).
If we expanded
(x + b)4
for example, then before adding the like terms, we would find term in
x4, x3b, x²b², xb3, and b4.
A binomial coefficient equals the number of combinations of r items that can be selected from a set of n items. It also represents an entry in Pascal’s triangle. These numbers are called binomial coefficients because they are coefficients in the Binomial theorem.
What the binomial theorem does is tell how many terms there are of each kind -- it adds those like terms. Those are the binomial coefficients.
We will see that determining those coefficients depends on the theory of combinations.
Binomial coefficient is intimately related to Bernoulli numbers, Catalán numbers, Fibonacci numbers, statistics and a host of combinatoric problems.
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