Question

Explain the significance of binomial coefficients with respect to Bernoulli trials.

Short answer

The number of outcomes that have exactly x number of successes in $\left(\begin{array}{c}n\\ x\end{array}\right)$Bernoulli trials is defined as the Binomial Coefficients.

Step-by-step solution

Step 1. Given information.

The given statement is:

Explain the significance of binomial coefficients with respect to Bernoulli trials.

Step 2. The significance of binomial coefficients with respect to Bernoulli trials.

Binomial Coefficients:

The binomial coefficient $\left(\begin{array}{c}n\\ x\end{array}\right)$is defined as follows:

$\left(\begin{array}{c}n\\ x\end{array}\right)=\frac{n!}{x!\left(n-x\right)!}$,

where n is a positive integer and x is a non-negative integer less than or equal to n.

As a result, the number of outcomes with exactly xsuccesses in "n" Bernoulli trials$\left(\begin{array}{c}n\\ x\end{array}\right)$ is known as the Binomial Coefficients.