Take human skin colour to be controlled by three genes, A, B and C.

The combinations. Each AaBbCc parent makes $8$ kinds of gametes in equal numbers, so there are $8 \times 8 = 64$ equally likely combinations. Each of a child's six alleles is dominant with a chance of $\frac{1}{2}$.

(a) Darkest. Only AABBCC, with all six alleles dominant: $\left(\frac{1}{2}\right)^6 = \frac{1}{64} = 1.56\%$.

(b) Classes. A child can have $0, 1, 2, 3, 4, 5$ or $6$ dominant alleles, so there are $7$ skin colours, from the lightest (aabbcc) to the darkest.

(c) Like the parents. The parents have three dominant alleles each. Three of the six alleles can be chosen in $20$ ways, so $\dfrac{20}{64} = 31.25\%$ of the children share this intermediate colour. It is the commonest class.

(d) Genotypes. Each gene gives three genotypes (for example AA, Aa and aa), so the three genes give $3 \times 3 \times 3 = 27$ genotypes.

(e) At least five dominant alleles. Five dominant alleles: $6$ ways; six: $1$ way. $\dfrac{6 + 1}{64} = 10.94\%$.