Example 4. The probability of hitting the target with a single shot is $p=0.8$. Find the probability of five hits in six shots.
Solution. We apply formula (3.2.1). Since by condition $n=6$, $k=5$, $p=0.8$, therefore, $q=1-p=0.2$, then

$$
\begin{gathered}
P_{6}(5)=C_{6}^{5} p^{5} q^{1}=\frac{6!}{5!} \cdot(0.8)^{5} \cdot(0.2)^{1}=6 \cdot(0.8)^{5} \cdot 0.2= \\
=6 \cdot 0.32768 \cdot 0.2=0.3934 .
\end{gathered}
$$