Question

A positive integer n is called strictly ascending if it's digits are in the increasing order. e. g. 2368 and 147 are strictly a ascending but 43679 is not. The number of strictly ascending numbers < 10^9 is
(A) 2^9 – 1
(B) 2^9
(C) 2^9 + 1
(D) 9!

Answer 1

The number of strictly ascending numbers = 501

Step-by-step explanation:

For a given set of unique digits there will be only 1 permutation which will give increasing order

0 can not be the digit as if 0 used it will not be ascending order

and there is no meaning of 1 digit number ascending or descending

2 Digits number  - ⁹C₂ = 36

3 Digit numbers = ⁹C₃ = 84

4 Digit numbers = ⁹C₄ = 126

5 Digit numbers = ⁹C₅ = 126

6 Digit numbers = ⁹C₆ = 84

7 Digit numbers = ⁹C₇ = 36

8 Digit numbers = ⁹C₈ = 8

9 Digit numbers = ⁹C₉ = 1

36 + 84 + 126  + 126 + 84  + 36 + 8 + 1

= 501

The number of strictly ascending numbers = 501

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