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Jelly, 28 bytes

"1⁄2Ṗ©cƘʂẒẹMMỤẓHP’Œ?"ðÑþQ’,ḥμÞ

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How it works

μ turns everything to its left into a monadic chain, which Þ maps over the input array and sorts the input according to the generated values.

"1⁄2Ṗ©cƘʂẒẹMMỤẓHP’ sets the return value to 176073885534954276199526358143331.

Œ? generates the 176073885534954276199526358143331^th permutation of the positive integers (without the sorted tail), yielding \$\small[20,28,15,3,5,26,18,16,8,30,4,25,2,21,22,11,24,1,23,10,29,12,17,27,14,9,6,13,7,19]\$.

"ðÑþQ’ yields 391695582; , prepends it to the permutation. Then, ḥc ompute Jelly's 391695582^th hash function, mapping the resulting buckets to the integers of the permutation.

The magic constant 391695582 was found by Jelly's utils.

dennis-home:utils$ time ./findhash 30 29 <<< '["red","yellow","green","brown","scarlet","black","ochre","peach","ruby","olive","violet","fawn","lilac","gold","chocolate","mauve","cream","crimson","silver","rose","azure","lemon","russet","grey","purple","white","pink","orange","blue"]'
391695582
real 0m2.058s
user 0m15.077s
sys 0m0.023s