Counting

 

Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $6,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)    

 

1 1 1 1 1 6      1 1 1 1 2 3      1 1 1 1 3 2     

1 1 1 1 6 1      1 1 1 2 3 1      1 1 1 3 2 1     

1 1 1 6 1 1      1 1 2 3 1 1      1 1 3 2 1 1 

1 1 6 1 1 1      1 2 3 1 1 1      1 3 2 1 1 1     

1 6 1 1 1 1      2 3 1 1 1 1      3 2 1 1 1 1     

6 1 1 1 1 1    

 

Looks like 16 ways to me, if I haven't missed any.     

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