Question

The genome of a diploid species has 10 genes. In a population of this species, if each gene has two unique alleles, then the number of possible unique genotypes in this population is ______ (Answer in integer)

Hint:

Work out how many genotype combinations are possible at a single gene locus with two alleles, then multiply that count across all the genes since they assort independently.

Answer 1

Correct Answer: 59049

Step 1: Count genotype options for a single gene.
Two alleles at one gene, say $A$ and $a$, give three combinations in a diploid: $AA$, $Aa$, $aa$. So one gene contributes a factor of $3$.

Step 2: Build up the total gene by gene.
Since the $10$ genes are separate and independent, multiply the factor of $3$ in, one gene at a time:
after 1 gene: $3$
after 2 genes: $3\times3=9$
after 3 genes: $9\times3=27$
after 4 genes: $27\times3=81$
after 5 genes: $81\times3=243$
after 6 genes: $243\times3=729$
after 7 genes: $729\times3=2187$
after 8 genes: $2187\times3=6561$
after 9 genes: $6561\times3=19683$
after 10 genes: $19683\times3=59049$

Step 3: Read off the final count.
Building the product one gene at a time across all $10$ genes lands on the same number as the shortcut $3^{10}$. \[ \boxed{59049} \]