Permutations and Combinations

Given digits 0,1,2,3,5,7
To find rank of 70513
Total number start with 1=5!=120
Number start with 2=5!=120
Number start with 3=5!=120
Number start with 5=5!=120
Number start with 701=6
Number start with 702=6
Number start with 703=6
‌70512=1
‌70513=1
Rank of 70513
‌=4×120+3×6+2
‌=500