pc 1

this is a very good question

this is same as the number of numbers between 0 and 1 with decimal points are non zero and decreasing..

assume that if we have 1 only.. then the number will be

1

if 2 and 1 then it will be
(1) + 1 = 2

if 3 and 2 and 1 then it will be 2+2=4

so for 9,8,...1 it will be 2⁸

I Hope the recurrsive logic is clear to everyone.

did i make a mistake in the reccursion?

yeah there is a better way and the answer is 2⁹-1

see each selection of distinct nos from the n digits 1... 9 will yeield one unique solution.. which isthe numbers put in decending order

So the number of ways will be 2⁹

out of this 1 way when we dont chose any..

hence 2⁹-1