The range of 3-digit numbers is 111-999 (889 numbers). Those ending in 6 are 116, 126, 136, ... 996. There are 89 of these. Those divisible by 6 are 126, 156, 186, ... 996. Divide this set by 6: 21, 26, 31, ... 166. There are N of these where f(N)=aN+b. When N=1, f(1)=21; N=2, f(2)=26. So 21=a+b and 26=2a+b, and a=5 and b=16, so f(N)=5N+16. When 166=5N+16, 5N=150 and N=30, so there are 30 multiples of 6 ending in 6 within the set of 3-digit numbers. So the probability is 30/889.