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A gene is a location of dna on a chromosome that encodes for a trait. An allele is a specific version of a gene that tells your body how to express the gene.
For instance, a chromosome could have a gene that determines eye color. The version of the gene that gives you blue eyes would be an allele, as would the version of the gene that gives you brown eyes.
Your body has many chromosome pairs, each chromosome in a chromosome pair have the same genes but they can have different alleles. People have two alleles for every gene. In the case of having different alleles on each chromosome, It is usually the case that there is one allele, called the dominant allele, which is expressed and the other allele, the recessive allele, is not expressed.
In the case of hair, the dominant brown hair allele would create melanin in a person's hair follicles and the recessive blond hair allele would be a dysfunctional version of the brown allele that does not create melanin. The end result of having one blond hair allele and one brown hair allele would be that the brown hair allele would create melanin and make your hair brown. In this case you would need 2 blond hair alleles to be blond, anyone with at least one brown hair allele would have brown hair.
Your cousin and her husband probably both had one copy of the blond hair allele and one copy of the brown hair allele. They had brown hair since the brown hair allele was dominant. When they mated, your cousin and her husband gave the kids their blonde hair alleles. So the kids have two blonde hair alleles (one from their mom, and one from their dad) and no brown hair alleles.
In actuality a person having blond/brown hair depends on many different genes but it's still the same idea.
