Chapter 8.4, Problem 3E

To determine

To find: binomial coefficients.

Explanation of Solution

There are two ways to find the binomial coefficients.

The first way to using Binomial theorem.

Binomial Theorem states that,

  ${\left(x+y\right)}^n=x^n+n{x}^{n-1}y+\mathrm{...}{+}_n{C}_r{x}^{n-r}{y}^r+\mathrm{...}+nx{y}^{n-1}+y^n$

The binomial expansion of any expression of form ${\left(x+y\right)}^n$ provides the binomial coefficients of each term of the expression.

The second way is using Pascal’s triangle.

Pascal’s triangle is a convenient way to calculate the binomial coefficients by arranging the coefficients in a triangular pattern.