CAT 2018 Slot 1 QA Question 15: How many numbers with two or more digits can be formed with the digits 1,2,3,4,5,6,7,8,9, so that in every such number, each digit is used at most once and the digits appear in the ascending order?

Question

How many numbers with two or more digits can be formed with the digits 1,2,3,4,5,6,7,8,9, so that in every such number, each digit is used at most once and the digits appear in the ascending order?

Accepted Answer

Once a set of digits is chosen, there is exactly one ascending number using those digits.
So, we need to choose any subset of size 2 or more from the 9 digits.
Number of required numbers $=C(9,2) + C(9,3) + ... + C(9,9)$
$=2^{9} - C(9,0) - C(9,1)$
$=512 - 1 - 9 = 502$