79% part.
The binomial distribution formula is given by
[tex]P(x)=C(n,x)p^xq^{n-x}[/tex]
where n is the number of randomly selected, x is the number of successes desired, p is the probability and q = 1-p is the probability of getting a failure.
In our case, p=0.79, q=1-0.79=0.21 and n is 8. Then, the scenario is given by
[tex]P(x)=C(8,x)0.79^x0.21^{8-x}[/tex]
now, we know that x is 6, then we have
[tex]P(6)=C(8,6)0.79^60.21^2[/tex]
where C(8,6) denote the combination formula:
[tex]C(8,6)=\frac{8!}{(8-6)!6!}=28[/tex]
Then, the probability is given by
[tex]\begin{gathered} P(6)=28\times0.24\times0.0441 \\ P(6)=0.296 \end{gathered}[/tex]
that is, the probability that exactly 6 are woman is 0.296
