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MHC class 1 receptors have different genes encoding it: HLA-A, HLA-B and HLA-C. Each gene come in two versions, mom and dad, so that is a total of 6 possibilities.

MHC is highly polygenic and polymorphic. HLA-A has 59 alleles, HLA-B has 111 alleles and HLA-C has 37 alleles. 59*111*37*6*2 = ~3 million combination. The odds that you will exactly match the same alleles as a donor is almost none. So they try to match several of the most important ones and even then it is very difficult. If your MHC's don't match well the organ receiver's adaptive immunity (specifically T cells) will recognize the transplanted organ as foreign and reject it.

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