# 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,…

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 are Y 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 Y2 sequences. For each of the Y2 sequences formed from 2 draws, there are Y ways the 3rd draw can occur forming Y3sequences. Generalizing, there are YX sequences 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 is 26 x 26 x 26 x 10 x 10 x 10 = 263 x 103 = 17,576,000. From this one style of plate, there are many sequences.

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