there should be 10 genotypes for part (a)
this question requires the use of the hardy-weinberg equilibrium (im not sure if this is explicitly part of the syllabus but it was in the textbook and we learnt it in class) - except the equation becomes p+q+r+s = 1 instead of just p+q=1 because there are more than 2 alleles on one locus here
so with 3 alleles, there are 1+2+3 = 6 genotypes
and with 4 alleles, there are 1+2+3+4= 10 genotypes
this is just an alternative but the equation posted by Hiva is basically the same