DNA permutations and combinations

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July 8th 2010, 11:13 AM
Felipe

DNA permutations and combinations

Can someone help me check if my work is correct?

Problem 1: Our genetic material, DNA, is formed from a 4 letter "alphabet" of bases: A, T, G, C (adenine, thymine, guanine, and cytosine). The order in which the letters are arranged is important, but because a molecule can move, there is no difference between a sequence and the same sequence reversed. For example, the sequence (A, A, T, A, G, A, T) is the same as the sequence (T, A, G, A, T, A, A). (In reality, DNA molecules have identifiable ends, but ignore that in this problem.)

How many distinct DNA sequences of 6 bases are there? (The answer to this particular question needs to be correct to one part in ten million.)

What I did was this: (4^6+4^6)/2 =4096

Is this correct? I don't get how "the answer to this particular question needs to be correct to one part in ten million" when my answer is only 4096

Any help would be greatly appreciated! Thank you!
July 8th 2010, 12:50 PM
p0oint

No, you need to do combinations with repetition.

$\binom{4 + 7 - 1}{7}=\binom{10}{7}=120$
July 8th 2010, 02:45 PM
awkward

Quote:

Originally Posted by Felipe

Can someone help me check if my work is correct?

Problem 1: Our genetic material, DNA, is formed from a 4 letter "alphabet" of bases: A, T, G, C (adenine, thymine, guanine, and cytosine). The order in which the letters are arranged is important, but because a molecule can move, there is no difference between a sequence and the same sequence reversed. For example, the sequence (A, A, T, A, G, A, T) is the same as the sequence (T, A, G, A, T, A, A). (In reality, DNA molecules have identifiable ends, but ignore that in this problem.)

How many distinct DNA sequences of 6 bases are there? (The answer to this particular question needs to be correct to one part in ten million.)

What I did was this: (4^6+4^6)/2 =4096

Is this correct? I don't get how "the answer to this particular question needs to be correct to one part in ten million" when my answer is only 4096

Any help would be greatly appreciated! Thank you!

Hi Felipe,

I don't follow your reasoning.

It seems to me you need to consider the following:

First, there are 4^6 possible sequences of bases if we don't worry about reversed sequences being equivalent.

Second, of these, 4^3 are palindromes-- the original sequence and the reversed sequence are the same. (Do you see why?)

So...