Question 952916
.
This problem is solved in 3 steps.


<U>Step 1</U>.


<pre>
How many are there 5 digit counting numbers in all ?


The answer is  9*10*10*10*10 = 90000,  because such a number can have

    - any of  9 digits from 1 to 9 in the mostleft position;
    - any of 10 digits from 0 to 9 in the 2nd position;
    - any of 10 digits from 0 to 9 in the 3rd position;
    - any of 10 digits from 0 to 9 in the 4th position;
    - any of 10 digits from 0 to 9 in the 5th position.


In all, there are 90000 such numbers.
</pre>


<U>Step 2</U>.


<pre>
How many are there 5 digit counting numbers that HAVE NO the digit 6 ?


The answer is 8*9*9*9*9 = 52488, because such a number can have

    - any of  8 digits from 1 to 9 except of 6 in the mostleft position;
    - any of  9 digits from 0 to 9 except of 6 in the 2nd position;
    - any of  9 digits from 0 to 9 except of 6 in the 3rd position;
    - any of  9 digits from 0 to 9 except of 6 in the 4th position;
    - any of  9 digits from 0 to 9 except of 6 in the 5th position.
</pre>


<U>Step 3</U>.


<pre>
Now the number under the problem's question is the difference 90000 - 52488 = 37512.
</pre>