Catherine rolls a standard 6-sided die six times. If the product of her rolls is \(2500 \) then how many different sequences of rolls could there have been? (The order of the rolls matters.)
\(\phantom{If the product of her rolls is 2700}\)
+131 The rolls must be 1, 2, 5, 5, 6 in some order, so there are 5!/2 = 60 ways.
There are more ways though. For example, there could be:
1, 3, 4, 5, 5
2, 2, 3, 5, 5
This gives another 90 ways:
1, 3, 4, 5, 5: 5!/2 = 60
2, 3, 3, 5, 5: 5!/4 = 30
If you add it with the previous one, we get 60+60+30 = 150
