## Submitted by Prerak Juthani

How many different alleles are there for a gene that is 1500 base pairs long such that each allele differs every other by exactly 1 base pair?

a) 4^1500

b) 1500 x 4

c) 1500^4

d) 60,000

e) None of the above

And the answer is…

B.

In this case, there are 1500 base pairs for you to change. For simplicity, let’s try the same question with 3 base pairs. In this case visualize the following: ____ _____ _____ (the lines to the left represent the 3 nucleotides). Now, we want to know the ways to manipulate the nucleotide sequence such that each one differs from the others at exactly one nucleotide. For one thing, you can manipulate JUST the first nucleotide and there are 4 ways to do that (because there are 4 possible nucleotides). Now, let’s think about how many ways we can change the second nucleotide; again, this is 4 because there are four possible nucleotides. And lastly, there are also 4 ways to change the last nucleotide. The total number of ways to have different versions of the same gene is the sum of these possibilities: 4 (changes in the first nucleotide) + 4 (changes in the second nucleotide)+ 4 (changes in the third nucleotides). These can then be added up because each change is mutually exclusive. Similarly, if we add this logic to this 1500 base pair region, then we get 4 + 4 + 4…. +4. Basically, we would get (4×1500), which means the answer is 6000.

In this case, there are 1500 base pairs for you to change. For simplicity, let’s try the same question with 3 base pairs. In this case visualize the following: ____ _____ _____ (the lines to the left represent the 3 nucleotides). Now, we want to know the ways to manipulate the nucleotide sequence such that each one differs from the others at exactly one nucleotide. For one thing, you can manipulate JUST the first nucleotide and there are 4 ways to do that (because there are 4 possible nucleotides). Now, let’s think about how many ways we can change the second nucleotide; again, this is 4 because there are four possible nucleotides. And lastly, there are also 4 ways to change the last nucleotide. The total number of ways to have different versions of the same gene is the sum of these possibilities: 4 (changes in the first nucleotide) + 4 (changes in the second nucleotide)+ 4 (changes in the third nucleotides). These can then be added up because each change is mutually exclusive. Similarly, if we add this logic to this 1500 base pair region, then we get 4 + 4 + 4…. +4. Basically, we would get (4×1500), which means the answer is 6000.