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Suppose a sample space has things a, b, and c. Twice,

/in /by

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 the 2 draws, there are Y ways the 3rd draw can occur forming Y3 sequences. Generalizing, there are Yx sequences formed by drawing X times from the Y different things with replacement.

How many sequences of 5 things can be formed from 8 different things with replacement and order is important?

 
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