If a given population of diploid organisms contains only three alleles of a particular gene (say, W1, W2, and W3), how many different diploid genotypes are possible in the population?

The correct answer is 6 genotypes

Explanation:

The most known case is two alleles of one gene (A and a), and we know the possible genotypes formed are three: AA, Aa, aa. Therefore, for a given number of alleles n, we calculate the number of possible genotypes as the sum of integers between 1 and n.

- For 2 alleles (n=2, the sum of integers between 1 and 2) : Genotypes = 1 + 2 = 3

⇒ For 3 alleles (n=3, the sum of integers between 1 and 3) : Genotypes = 1 + 2 + 3 = 6

So, we have 6 genotypes for 3 alleles (W1, W2 and W3) and they are:

W1W1

W1W2

W1W3

W2W2

W2W3

W3W3