Counting

Catherine rolls a standard 6-sided die six times. If the product of her rolls is 200, then how many different sequences of rolls could there have been? (The order of the rolls matters.)  

The prime factorization of 200 is 2 x 2 x 2 x 5 x 5 but  

that's only five factors and Cat rolled six times so we  

need to add a 1 to the rolls. 

She had to roll these numbers:  1, 2, 2, 2, 5, 5     

How many sequences of these could have occurred.  

The permutation of six things taken six at a time.  

                            ₆P₆ = 720

Oh, she could have rolled 1, 1, 4, 2, 5, 5  etc.      

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