Question

Why are combinations used in the binomial theorem for it's coefficients?​

Answer 1

In short, the reason we use combinations is because the order does not matter, because we will get terms like aab,baa,bab which are all equal in the expansion. Since multiplication is a commutative operation over the real numbers, then, we can say they're equal.

ADDITIONAL INFORMATION:

How Do you Use NCR Formula in Probability?

• Combinations are a way to calculate the total number of outcomes of an event when the order of the outcomes does not matter. To calculate combinations we use the nCr formula: nCr = n! / r! * (n - r)!, where n = number of items, and r = number of items being chosen at a time.

SOME MORE:

• In combinatorics, the binomial coefficient is used to denote the number of possible ways to choose a subset of objects of a given numerosity from a larger set. It is so called because it can be used to write the coefficients of the expansion of a power of a binomial.

• 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.

• The combination (nr) is called a binomial coefficient. An example of a binomial coefficient is (52)=C(5,2)=10 ( 5 2 ) = C ( 5 , 2 ) = 10 .

Answer 2

Answer:

In short, the reason we use combinations is because the order does not matter, because we will get terms like aab,baa,bab which are all equal in the expansion. Since multiplication is a commutative operation over the real numbers, then, we can say they're equal.