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When 'Aa' combine with 'Aa', the number of possible combinations is 3

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When 'AaBb' combines with 'AaBb' the number of possible combinations is:

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I hope I didn't make any mistakes, but you get the idea.

How many combinations if I have 15 characters? 'AaBbCcDdEe...'. The answer is $3^{15}$ but why?

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    In the example given, Aa and aA are obviously assumed to be the same. However, a sequence of genes (or simply switches that can hve two states) would result in the following: AA, Aa, aA and aa2013-02-02

1 Answers 1

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Terminology: I'll refer to {AA, Aa, aa} as the character pairs for the letter A (and similarly for other letters).

The possibilities for each character pair in the combinations of $n$ character pairs are independent. So the total number of combinations is the product of the the number of combinations for each character pair. In this case, they are all the same, since which letter you use does not affect how many pairs you can get.