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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?

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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.

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