Question

The number of rational numbers lying in the interval $(2002,2003)$ all of whose digits after the decimal point are non-zero and are in decreasing order is

• A. ${\sum }_{i=1}^{9}9P_i$
• B. ${\sum }_{i=1}^{10}9P_i$
• C. $2^9-1$
• D. $2^{10}-1$

Answer 1

Answer: (C)

$2^9-1$

Non zero and decreasing order - That means we just have to choose any number of digits from 1 - 9 (without repetition), then there is only one way to form the rational number.

$\therefore$ No. of rational numbers in
${}^9{C}_1+{}^9{C}_2+.......+{}^9{C}_9=2^9-1$