Question: How many sequences of five things can be formed from nine different things with replacement and order is important? Suppose a sample space has things

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

Suppose a sample space has things a, b, and c. Twice, draw from the sample space and replace. The possible sequences formed are Iaa, 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 Yways 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 Yways the 3rd draw can occur forming Y3 sequences. Generalizing, there are YE 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 = 1?,5?6,DU{'}. From this one style of plate, there are many sequences

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