Rhodesian ridgebacks can have one of two nose colours: black or brown (usually referred to as "liver"). The eye colour should be in line with the colour of the dog: the liver nose should be accompanied by an amber eye colour; the black nose should have a dark eye colour. Liver noses can vary in the intensity of their nose pigment, from a deep brown to a light, almost pinkish color. Both - black nose and liver nose - are correct according to the standart of the breed.
Parents give to their offspring one of the two alleles from each parent. The set of alleles for a given organism is called its genotype, while the observable traits of the organism are called its phenotype. If two alleles of a given gene are identical, the organism is called a homozygous; if instead the two alleles are different, the organism is heterozygous. When organisms are heterozygous at a gene, one allele is called dominant as its qualities dominate the phenotype of the organism, while the other allele is called recessive as its qualities recede and are not observed. Concerning noses of ridgebacks, black color is dominant, while liver is recessive.
The livernose is seen less often than black nose simply because it is a recessive feature. Both parents must have the liver gene and pass it on to their progeny in order to produce livernosed puppies. Black nosed ridgebacks can produce liver puppies if they carry a copy of the liver gene along with the dominant gene for black; to produce livernose puppies, they must be bred to either a livernose or another heterozygous black nose – that is, one that also carries the livernose gene. Two homozygous black nose ridgebacks will not produce liver puppies.
Schematic information about inheritance of livernose you can find in the attached pdf file.
Griffiths, William M.; Miller, Jeffrey H.; Suzuki, David T. et al, eds. (2000). "Interactions between the alleles of one gene". An Introduction to Genetic Analysis (7th ed.). New York: W. H. Freeman.
King et al., RC (2006). A Dictionary of Genetics. Oxford University Press.