Answer:
B. This gene mutation is a dominant disorder.
Step-by-step explanation:
Since all the children in generation III do not have the disorder, there is no indication that all the children born in the future generations will be affected by this disorder.
The gene mutation appear dominant from the pattern of inheritance. The children in generation II are all affected because there are two dominant alleles for the disorder in the father. Some of the children in generation III do not have the disorder because only one allele is dominant in the mother, hence, the unaffected children inherited the non-dominant allele from the mother.
The gene mutation is not recessive, otherwise, not all the offspring in generation II are supposed to be affected for the disorder.
The mother in generation I cannot be a carrier because the disorder is a dominant one. There can only be heterozygous for a dominant disorder but they are usually phenotypically affected for the disorder.
The correct option is B.