Suppose a sample space has things a, b, and c. Twice, draw from the sample space and replace. The possible sequences formed are {aa, ab, ac, ba, bb, bc, ca, cb, cc}.

Now suppose there areY different things.There are Y ways the first draw can occur. For each of the Y ways the first draw can occur, there are Y ways the second draw can occur, resulting in Y times Y, or Y²sequences. For each of the Y²sequences formed from 2 draws, there are Y ways the 3rd draw can occur forming Y³sequences. Generalizing, there are Y^Xsequences formed by drawing X times from Y different things with replacement.

Example:The number of state license plates that can be made with 3 letters followed by 3 numbers is26 x 26 x 26 x 10 x 10 x 10 = 26³x 10³= 17,576,000. From this one style of plate,there are many sequences.

How many sequences of 4 things can be formed from 8 different things with replacement and order is important?