I am looking at the following question
If $m$ alleles may occur at a given locus, how many distinct diploid genotypes are possible at that locus?
The obvious answer is that there their is $m$ possible paternal alleles and $m$ possible maternal alleles so the solution is $m^2$. However this considers inheriting allele $a$ maternally and allele $A$ paternally as the same as inheriting $a$ paternally and $A$ maternally.
If they are considered distinct we have double counted all matchings apart from matchings where the same allele is inherited maternally and paternally so I think the answer to the question if $Aa$ is the same as $aA$ would be $\frac{m(m-1)}{2}+m$
My question is which if any of my interpretations is correct?
Thanks in advance