Since the 5 hits can be any of the 7 attempts, we first need to calculate a combination of 7 choose 5.
The formula for a combination of n choose p is:
[tex]C(n,p)=\frac{n!}{p!(n-p)!}[/tex]
So we have:
[tex]C(7,5)=\frac{7!}{5!(7-5)!}=\frac{7\cdot6\cdot5!}{5!\cdot2!}=\frac{7\cdot6}{2}=21[/tex]
Now, if the probability of hitting is 0.28, the probability of missing is 1 - 0.28 = 0.72
Then, for the final probability, we can use the formula:
[tex]\begin{gathered} P=C(7,5)\cdot(0.28)^5\cdot(0.72)^2 \\ P=21\cdot(0.28)^5\cdot(0.72)^2 \\ P=0.0187 \end{gathered}[/tex]
So the probability is 0.0187.
