Final answer:
The pattern of inheritance described in the question is likely X-linked recessive, where an affected father passes the disorder onto his son and a carrier but unaffected daughter.
Step-by-step explanation:
The scenario described suggests that the genetic disorder in the family is likely inherited through an X-linked recessive pattern. In this type of inheritance, males, who have only one X chromosome, will express the disorder if they inherit the affected X chromosome, since they don't have a second X chromosome to mask the effect of the recessive gene. Therefore, they cannot be carriers and are either affected or not based on the single X chromosome they possess.
Daughters, on the other hand, have two X chromosomes. They can be carriers if they inherit one affected X chromosome, but they generally do not display the disorder unless they inherit affected X chromosomes from both parents. Given the information that the father is affected (has the disorder) and the mother is presumably not mentioned to be a carrier or affected, the daughter has inherited one normal X chromosome from the mother and one affected X chromosome from the father, making her a carrier but not affected. The son, however, has the disorder since he inherited the affected X chromosome from his father and does not have another X chromosome to compensate for it.