Question

How many five-digit numbers are there in whose notation each successive digit exceeds its predecessor?

Answer 1

the answer is the number of ways in which we can select 5 different digits out of 0 to 9 since if they are different we can make a single number in the ascending order but we have to consider that if we take 0 at first it will be a 4 digit number

from $1$ to $9$ we can select $5$ numbers in $9_{C_5}=126$ ways

now if we take 0 it must be kept at first according to the question so we shoulldnot take 0, therefore, the answer is 126