The binomial for this situation is $(p + q)^5$ because there are
five children in the family ($n = 5$). The expansion of this
binomial is
$(p+q)^5 = p^5 + 5p^4q + 10p^3q^2 + 10p^2q^3 + 5pq^4 + q^5$
Each of the terms in the expansion provides the probability
of one particular combination of traits in the children. The
first term in the expansion ($p^5$) equals the probability of hav-
ing five children with albinism because $p$ is the probability
of albinism. The second term ($5p^4q$) equals the probability
of having four children with albinism and one with normal
pigmentation, the third term ($10p^3q^2$) equals the probability
of having three children with albinism and two with normal
pigmentation, and so forth.
To obtain the probability of any combination of events, we
insert the values of $p$ and $q$. Thus, the probability of having
two out of five children with albinism is
$10p^2q^3 = 10 \left(\frac{1}{4}\right)^2 \left(\frac{3}{4}\right)^3 = \frac{270}{1024} = 0.26$
