pranavanmaru

I was browsing the web to find intriguing questions for quant section especially in Combinatorics. Bumped on to the following question. How many ternary strings of length 4 have exactly one 1? [Courtesy : http://web.eecs.utk.edu/~booth/311-04/notes/combinatorics.html] My answer for this question was, _,_,_,_ 4 spaces needs to be filled with 0,1 and 2 out of which one of them needs to be 1. there are 4 ways in which one of them could be 1 and in all other instances there would be choices of 2 numbers in filling 3 of these blanks 4*(23) 32 strings have exactly one 1 in it. According to the site where i got this question from though, the answer is different. [3*(23)] Can anyone clarify what's the logical fallacy in my answer? or elaborate more on why it could be wrong?