Question 952916


We can divide all the five digit numbers into two groups.

One group which contains all such numbers which do not have {{{6}}} at all, and the other group will be of such numbers which have at least one {{{6}}}. 
These two groups or sets are complementary to each other. They together make the set of all {{{5 }}}digit numbers.

It is easy to calculate the number of {{{5}}} digit numbers which do not contain {{{6}}} at all. If we calculate this number and subtract it from the total number of {{{5}}} digit numbers, we will get the required answer.

The total number of 5 digit numbers => {{{99999 - 9999 = 90000}}}.

Out of these, the number of 5 digit numbers which do {{{not}}} contain {{{6}}} at all is equal to:
 
{{{9*9*9*9*9 =9^5= 59049}}} (9 digits for each placeholder) 

Therefore the number of five digit numbers which contain at least one {{{6}}} is: 
{{{90000 -59049 = highlight(30951)}}}