The number of rational numbers lying in  the interval (2015, 2016) all whose digits after the decimal point are non-zero and are in decreasing order is

A rational number of the desired category is  of the form 2015. x1x2…xk and 9 ≥ x1 > x2 > … > xk ≥ 1. We can choose k digits out 9 in  9Ckways and arrange them in de creasing order in just one way. Thus, the desired number of rational numbers is  9C1+9C2+…+  9C9=29−1