I have a combinatorics problem, and I am not sure of my answer, which seems stupidly large. Could anyone spot the mistake?
I have a set of $7$ unique elements. First, I need to know how many permutations I can get out of those $7$ elements.
(e1, e2, ....)
(e2, e1, ....)
If I am not mistaken, the answer is $7!$.
For each permutation, each element can take a certain number of value:
e1: 1 value
e2: 1 value
e3: 9 values
e4: 13 values
e5: 17 values
e6: 51 values
e7: 51 values
How many possible combination of $7$ values can I get?
e.g. If the permutation set is (e1, e3, e2, e5, e6, e4, e7), I could get:
(e1.val1, e3.val5, e2.val1, e5.val17, e6.val32, e7.val44)
I think it is:
7! * (9*13*17*51*51)
Then for each possible combination, $500$ steps are required (by an algorithm). Thus, the total number of steps performed is:
7! * (9*13*17*51*51) * 500
If I had run this program on a powerfull workstation, I would have taken that number. But trillions of steps performed by my laptop in a few days seems a bit large.
No everything is correct. Note that final value you get is ca. $1.30\times 10^{13}$, which is a formidable number.