You can put this solution on YOUR website! It is the sum of 10C1...10C10
for 1:10+10 10C9------------20+90+240+420+252+1=1023 subsets with at least one element.
for 2:45+45 10C8
for 3:120+120 (10C7)
for 4:210+210 (10C6)
for 5:252
for 10:1
OR...2^10-1