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Combinatorics - Counting


pranavanmaru

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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?

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