Find the probability of the following  

$(i)$ to roll a $1$,then a $2$ and then a $3$ on consecutive roll of a single dice,  

$(ii)$to roll three identical dice and have the outcome be a $1$,a $2$ and a $3$.  

Which is more likely with perfect six-side dice?  

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My Attempt:  

Probability to roll a $1$,then a $2$ and then a $3$ on consecutive roll of a single dice$=\frac{1}{6}\times\frac{1}{6}\times\frac{1}{6}+\frac{5}{6}\times(\frac{1}{6})^3+(\frac{5}{6})^2\times(\frac{1}{6})^3+(\frac{5}{6})^3\times(\frac{1}{6})^3+.....$  

$=\frac{1}{36}$  

Probability to roll three identical dice and have the outcome be a $1$,a $2$ and a $3=\frac{6}{216}=\frac{1}{36}$  

There are 216 sample points in the sample space when we throw three dices and record the outcomes.Out of them six are favourable.$(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)$  

So the two events are equally likely.  

But the book answer says $(ii)$ event is more likely.I dont know how.Is some mistake i have made.Please help me.