find the probability of exactly three successes in eight trials of a binomial experiment in which the…

find the probability of exactly three successes in eight trials of a binomial experiment in which the probability of success is 45%. p(3) = $_8c_3(0.45)^3(0.55)^{8 - 3}$ solve part of the answer. $_8c_3=?$

find the probability of exactly three successes in eight trials of a binomial experiment in which the probability of success is 45%. p(3) = $_8c_3(0.45)^3(0.55)^{8 - 3}$ solve part of the answer. $_8c_3=?$

Answer

Explanation:

Step1: Recall combination formula

The combination formula is ${n}C{r}=\frac{n!}{r!(n - r)!}$, where $n = 8$ and $r=3$.

Step2: Calculate factorial values

$n!=8! = 8\times7\times6\times5\times4\times3\times2\times1$, $r!=3!=3\times2\times1$, and $(n - r)!=(8 - 3)!=5!=5\times4\times3\times2\times1$.

Step3: Substitute into formula

${8}C{3}=\frac{8!}{3!(8 - 3)!}=\frac{8\times7\times6\times5!}{3\times2\times1\times5!}$.

Step4: Simplify the expression

The $5!$ terms cancel out. Then $\frac{8\times7\times6}{3\times2\times1}=\frac{336}{6}=56$.

Answer:

56