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In how many ways can four different amino acids be arranged into a polypeptide chain of five amino acids?
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As far as I know, at this forum, no one of our tutors is biologist or molecular biologist, or biochemist, or organic chemist.
Therefore, I will not answer your question, as it is posed in the post.
I will answer another question.
In how many different ways 4 different items can be distributed in 5 different boxes
having no more than one item per box?
The answer is 5*4*3*2 = 120 different ways, by placing
item 1 in any of 5 boxes,
item 2 in any of remaining 4 boxes,
item 3 in any of remaining 3 boxes,
item 4 in any of remaining 2 boxes.
It would be interesting to me to learn it from you, if my response/solution really answers your question.
PLEASE let me know.