An increasing number has its digits increase in size from left to right. For example, 24589 is an increasing number. How many four-digit increasing numbers are there?
There are 10C4 ways to choose 4 digits that is 210 ways
Now for each of these combiations there is exactly 1 where the digits are in ascenting order.
So that is still 210 ways.
If you discount numbers beginning with 0 then that gets harder.
Lets see... if the first one is 0 how many ways can the others be chosen. 9C3=84 ways
So I think there are 210-84= 126 ways
So there are 126 numbers that meet this criterion.