Question

How many whole numbers are there with not more than 4 digits?

Answer 1

 when I say "place 1" I mean the first digit reading left to right. 

7000 has 7 in place 1 
1700 has 7 in place 2 
1170 has 7 in place 3 
1117 has 7 in place 4 

Answer 2

List them in a table. Note that the diagonal will not count.
xx 13 15 17
31 xx 35 37
51 53 xx 57
71 73 75 xx
Counting you get 12.

By reasoning:

There are 4ways to pick the first digit and 3 ways to pick the second digit. 12 ways.


This way can be extended to more digits in the number and uses the combinatorial and factorial functions.

There are 4C2 ways to pick any two digits. There are two factorial ways (13 and 31 to make a number with them.)
2! times 4C2. = 2! times ( 4 times 3 divided by 2) = 12.