How many telephone numbers that are seven digits in length have exactly five 6's? How many phone numbers that are seven digits in length, have exactly five 6's?
My attempt: {{6,6,6,6,6}{ , }}
$(5(top) 5(bottom)) * (18(top) 2(bottom)) = 153$
my reasoning is that the first subset containing the 6's must all be 6, so when I do the permutation I get 1, now on the second subset, there are 18 numbers remaining (9+9) since 6 is not allowed and I can only pick two, so when I do the permutation i get 153.
so 1*153=153.
However, I feel like this is wrong, if so can someone point me down the right direction? 

The locations of the $6$'s can be chosen in $\binom{7}{5}$ ways. For each such choice, the remaining two slots can be filled in $9^2$ ways.
