How many possible genotypes are there with 3 loci where each locus has 11 allele

Question

How many possible genotypes are there with 3 loci where each locus has 11 alleles and the loci are independent? For heterozygotes, the order of the alleles doesn't matter (so, treat Aa and aA as the same genotype). When calculating the allelic combinations, the formula is slightly different than what was shown in Dr. Eckert's video, as it seems that repetition (i.e. homozygous) weren't taken into account. You'll want to use this formula: (r + n - 1)!/r!(n - 1)! Then don't forget to take that number and apply the appropriate formula for the number of loci. If you cannot see the image. it's(r + n - 1)!/r!(n - 1)! where r is the same as k in the video). For more info, here's a helpful website: (http://www.mathsisfun com/combinations/combinations-permutations, html) You can still use the other formula if that is what you're most familiar with - you just need to add in the extra set of homozygotes once you get your answer for the allelic combinations. Then don't forget to apply the appropriate formula for the number of loci.

Explanation / Answer

Given that the number of alleles, n = 11

number of loci, r = 3

Substitute the above values in the formula, (r+n-1)! / r!(n-1)!

The number of allele combinations is = (3+11-1)! / 3! 10! = 286.

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