Permutations

Question

A six-sided number cube is rolled three times. How many outcomes are possible?

Answer 1

Often, the instruction on "how many possibilities" starts with something well-known -- the decimal system.  Think of an odometer (PLZ learn what this is if you want to drive someday) or a gas pump or a bicycle lock or a briefcase lock or an electricity meter ...

 

An odometer's dials go from 0 to 9 then again from 0 to 9 then again grom0 to 9 ...   A new cycle for each single new digit at the next higher level.  So, we count from 000 to 999 and there are 1000 unique numbers.

 

For a cube (6-sided), each roll goes from 1-6.  Thus, we start at 111, then 112. 113. 114. 115. 116. 121. 122 ...

Notice that we start over after 6, so there are 6*6*6 = 216 three-digit numbers possible.  It is important to note that each roll of the cube behaves independently, has an equal chance of producing each number as an outcome (a "fair" cube), and that duplicate numbers are allowed.  [note: you may learn formulas for other situations later]