Question

In 10 Bernoulli trials, how many outcomes contain exactly three successes?

Short answer

In 10 Bernoulli trials, 120 outcomes contain exactly three successes.

Step-by-step solution

Step 1. Given information.

The given statement is:

In 10 Bernoulli trials, how many outcomes contain exactly three successes?

Step 2. Find the outcomes contain exactly three successes 

Total no. of trials (n): 10

Number of success needed (p): 3

Then the number of outcomes contains exactly three successes:

$$\begin{gathered} \left(\begin{array}{c}10\\ 3\end{array}\right)=\frac{10!}{3!\times \left(10-3\right)!} \\ =\frac{10!}{3!\times 7!} \\ =\frac{10\times 9\times 8}{3\times 2\times 1} \\ =120 \end{gathered}$$