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Sorry for posting twice in sucession, I was going to add this question in the same post as my previous one, but somehow forgot. Also, if you aren't going to explain an answer, I won't learn and I might as well not have the answer anyway. (I'm looking at you, guest troll.)

Anyways here is the question.

Catherine rolls a 6-sided die five times, and the product of her rolls is 300. How many different sequences of rolls could there have been? (The order of the rolls matters.)

 May 23, 2021
 #1
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The rolls must be 1, 2, 5, 5, 6 in some order, so there are 5!/2 = 60 ways.

 May 23, 2021
 #2
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There must have the orders of factors, 

5 5 4 3 1: 5!/2! =60

5 5 3 2 2: 5!/2!2! =30

6 5 5 2 1: 5!/2! =60

60+30+60=150

150 is the answer.

 May 23, 2021

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