# Phenotype-Genotype for multi-hybrid crosses

It's generally easy to figure out genotype and phenotype frequencies using a Punnett square for monohybrid and Dihybrid crosses. But what about situations involving 5 or 6 traits? Is there a simpler way to get about this?

As a sample problem: If we have two organisms crossed, one with genotype AaBBcCddEe and the other with genotype aaBBccDdEe (lowercase is recessive and upper case is dominant), how many individuals would have the genotype AaBBCcDdEE?

In my opinion, the easier way is dealing with each trait separately, as if it was a simple monohybrid cross, and writing down each result:

1. Aa x aa → $\frac{1}{2}$ Aa;
2. BB x BB → 1 BB;
3. Cc x cc → $\frac{1}{2}$ Cc;
4. dd x Dd → $\frac{1}{2}$ Dd;
5. Ee x Ee → $\frac{1}{4}$ EE;

Now, simply multiply all the results:

$\frac{1}{2} * 1 * \frac{1}{2} * \frac{1}{2} * \frac{1}{4}$ → $\frac{1}{32}$

I don't know about your country, but in my country of birth all secondary books have a chapter for monohybrid cross and another chapter for dihybrid cross. I don't like that, it creates a nonexistent separation and it makes (some) students memorize concepts. Linkage apart, I like to say to my students to do not mind about dihybrid, trihybrid, tetrahybrid etc crosses, just treat them as individual monohybrid crosses combined.