To solve this problem, we need to determine the possible genotypes and phenotypes of the children based on the given genotypes of the parents.$\newline$The genotypes of the husband and wife are $I^{A}I^{B}$ and $I^{A}i. \newline$Let's determine the possible genotypes of their children:$\newline \bullet$The possible alleles from the husband $(I^{A}I^{B})$ are $I^{A}$ and $I^{B}. \newline \bullet$The possible alleles from the wife $(I^{A}i)$ are $I^{A}$ and $i. \newline$Using a Punnett square, we can find the possible genotypes of the children:$\newline \bullet$Possible genotypes:$\newline$ - $I^{A}I^{A}$ (from $I^{A}$ of husband and $I^{A}$ of wife)$\newline$ - $I^{A}I^{B}$ (from $I^{A}$ of husband and $I^{B}$ of wife)$\newline$ - $I^{A}i$ (from $I^{A}$ of husband and $i$ of wife)$\newline$ - $I^{B}i$ (from $I^{B}$ of husband and $i$ of wife)$\newline$Thus, there are 4 different genotypes possible.$\newline$Now, let's determine the phenotypes corresponding to these genotypes:$\newline \bullet$Genotype $I^{A}I^{A}$ results in blood type A.$\newline \bullet$Genotype $I^{A}I^{B}$ results in blood type AB.$\newline \bullet$Genotype $I^{A}i$ results in blood type A.$\newline \bullet$Genotype $I^{B}i$ results in blood type B.$\newline$Thus, there are 3 different phenotypes possible: A, B, and AB.$\newline$Therefore, the correct answer is:$\newline$Option 2: 4 genotypes; 3 phenotypes.