Permutations are the management of items in an orderly manner, this focuses on the order of the items. In the given case, the order of the amino acids matters to find out the number of combinations.

The formula is:

nPr = n! / (n-r)!;

where,

n = number of elements
r = number of elements required in each set.

Permutation formula applied in this case:

$^{n}P_{r}=\dfrac{n!}{(n-r)!}^{10}P_{10}=\dfrac{10!}{(10-10)!}^{10}P_{10}=\dfrac{10\times 9\times 8\times 7\times 6 \times 5\times 4\times 3\times 2\times 1}{0!}\\^{10}P_{10}=\dfrac{3628800}{1}\\^{10}P_{10}=3628800$

Thus, the number of combinations for a protein that’s 10 amino acids long would be - 3628800

Learn more about amino acids:

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