Different seven-digit numbers could Sid have meant to type 
Sid intended to type a seven-digit number, but the two 3's he meant to
  type did not appear. What appeared instead was the five-digit number
  $52115$. How many different seven-digit numbers could Sid have meant to type?

First time, I attempted this problem as follows-
I considered, there are 12 places available for two 3's (as they can appear together)
_ _ 5 _ _ 2 _ _ 1 _ _ 1 _ _ 5 _ _
So, we can select 2 places from 12 places in ${12\choose 2}$ = $66$ ways.
But, I found the correct approach is simply choosing 2 places from available 7 place in ${7\choose 2}$ = 21 ways. However, I can't find my mistake in previous one. Can anyone explain what am I missing?

Consider the following possibilities:
_ 3 5 _ _ 2 _ _ 1 _ _ 1_ _ 5 _ 3
_ 3 5 _ _ 2 _ _ 1 _ _ 1_ _ 5 3 _
3 _ 5 _ _ 2 _ _ 1 _ _ 1_ _ 5 _ 3
3 _ 5 _ _ 2 _ _ 1 _ _ 1_ _ 5 3 _
All of these would give the same result of 3521153, but are counted separately by your first method.
