Physics/probability question

[chuckywang]

Originally posted by: Eeezee
I'll do some google searching to see if I can better understand it. It sounds fairly complicated. Thanks for your help 🙂

Probability really tests your critical thinking skills. It's good for your brain.

 

[Eeezee]

The professor isn't going to tell me if this is correct until more students e-mail him with responses. Are we certain that it's +20^500 and not -20^500? I was thinking that it should be -, but you guys know more than me about this topic so I went with +.

 

[Hyperion042]

He's wrong on a technicality, actually.

In reality, you don't divide by 2 for a protein. See, proteins have an inherent order to their sequence due to the fact that on one end of the protein, you have a carboxylic acid, and on the other terminal you have an amine. Chemically, these are distinct - as a result, the two proteins ABB and BBA ARE NOT equivalent. They're just ~mostly~ equivalent - in reality, they aren't one and the same. If you ignore the fact that proteins can't be read the same backwards as forwards, though, the answer is (20^1000-20^500)/2.

 

[randay]

just bone her to get your extra credit, worked for me!

 

[chuckywang]

Originally posted by: Eeezee
In particular, why is there an additive term of 20^500 * 1/2? Where did this number originate?

There are 20^500 total palindromes.
There are 20^1000 total links.

Therefore, there are 20^1000-20^500 non-palindrome links. For the reasons discussed, there are 1/2*(20^1000-20^500) proteins of non-palindrome links.

Add on the 20^500 palindromes (since they are a protein all their own), and you get:

1/2*(20^1000-20^500)+20^500 = 1/2*(20^1000 + 20^500).

No group theory necessary.