Please show your work so I can understand how you got your a

Please show your work so I can understand how you got your answer!

There are about ~25,000 genes in the human genome. If you wanted to use a stretch of the DNA from each gene as a unique identification tag, roughly what minimum length of DNA sequence would you need? To be unique, the length of DNA in nucleotide must have a diversity (the number of different possible sequences) equivalent to at least 25,000 and would have to be present once in the haploid human genome (3.2x10⁹ nucleotides)? (Assume that A,T,C and G are present in equal amounts in the human genome)

Solution

Since all four bases are present in equal amount and teh haploid human genome has 3.2 x 10⁹ nucleotides; a sequence,expected to be present once in haploid genome of human can be given as following:

4¹⁵ = 1.1 x 10⁹ bases
4¹⁶ = 4.3 x 10⁹ bases

This means that a 16 nucleotides long sequence occurs once. So,the minimum length for a unique identification tag for a gene in the human genome is 16 nucleotides long.