A 7 digit number is formed by arranging the digits 1,2,2,3,6,6,6. What is the probability the number formed is larger than 3,000,000?

Can someone tell me if my approach makes sense/and or is correct. 

So in order to be greater than 3,000,000 the first digit needs to be a 3,6,6,6 so there are 4 options for the first spot and then count down for the rest so 4x6x5x4x3x2x1 then for all total arrangements that would be 7! so the probability is 2880/5040. Is that correct?