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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.)

 Oct 16, 2024
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You could have 5 ones and a 6.  The six can be any of the tosses so that is 6 ways   (for 6 tosses.)

 

Or you could roll a 2, a 3 and four 1's  in any order.

 

you have 1 1 1 1 there are 5 places where you can slot in a 2 

 

Now you have     X X X X X    where one of the x's is a 2 and the others are all 1s.

 

There are 6 ways to now slot in the 3.

 

Than makes    5*6 = 30 ways to have a 2, a 3 and four ones.

 

30+6  - 36 possibilities.

 

I think that is correct.

 Nov 21, 2024

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