Question

how many positive integers have digits that are increasing left to right? for instance, 123 and 5789 are examples, but 621 and 15578 are not

Answer 1

Answer:

ere're my thoughts on the problem.

For one digit numbers.

There are only 9 such integers that satisfy the problem.

For two digit numbers.

If we start with 1 as the left most digit, then we have 8 choices for the one's place. So we have 8 such numbers.

If we start with 2 as the left most digit, then we have 7 choices for the one's place.

If we start with 3 as the left most digit, then we have 6 choices for the ones place.

Continuing this process we have 8+7+6+...+2+1=36 such numbers.

But for three - digit numbers, I'm stuck. What am I suppose to do, after I've chosen the first digit? I'll have to make sub cases for the second digit, and it'll get more complicated as I go up to 9 - digit numbers.

Step-by-step explanation: