Answer
$P(X=3)=C(5,3)*0.1^3*0.9^2=\frac{5!}{3!\times(5-3)!}\times0.1^3\times0.9^2=0.0081$
Work Step by Step
The solution is based on the binomial distribution:
$P(X=x)=C(n,x)*p^{x}*q^{n-x}$
If we perform 5 independent Bernoulli trials, and $p=0.1$, the probability of threesuccesses are:
$C(5,3)*0.1^3*0.9^2$.
As there are 5 trial out of which three are successes. And the probability of a success is 0.1.
$P(X=3)=C(5,3)*0.1^3*0.9^2=\frac{5!}{3!\times(5-3)!}\times0.1^3\times0.9^2=0.0081$
