How many telephone numbers that are seven digits in length have exactly five 6's?

Question

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?

Answer 1

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.