Question

nPr=3024,then how to calculate the value of r?

Answer 1

The solution is not determined. One possible set of values is n=3024, r=1.

Answer 2

To find other solutions you can try factoring the number to prime decomposition. This produces 7*(3^3)*(2^4). We want to group these so that the resulting grouped factors are descending by increments of 1. I can see already that we can get 9 (=3^2) and 8 (=2^3) and there's a 7. The remaining factors are 3 and 2, which group together and make 6. Thus we have a good descending order, 9*8*7*6. This is 9P4, so another value of r is 4.

I conjecture that this is the exhaustive set of solutions for r.