Suppose a sample space has things a,b, and c Twice, draw from the sample and replace The possible sequences formed are (aa,ab,ac,ba,bb,bc,ca,cb,and 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 Y 2 sequences For each of the Y 2 sequences formed from 2 draws, there are Y ways the 3rd draw can occur forming Y 3 sequences Generalizing, there are Y X 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 26x26x26x10x10x10 26 3 x10 3 17,576,000 From this one style of plate, there are many sequences How many sequences of 4 things can be formed from 9 different things with replacement and order is important

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Question: Suppose a sample space has things a,b, and c. Twice, draw from the sample and replace. The possible sequences formed are (aa,ab,ac,ba,bb,bc,ca,cb,and cc). Now suppose

Suppose a sample space has things a,b, and c. Twice, draw from the sample and replace. The possible sequences formed are (aa,ab,ac,ba,bb,bc,ca,cb,and 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 Y³ sequences. Generalizing, there are Y^X 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 26x26x26x10x10x10= 26³x10³=17,576,000. From this one style of plate, there are many sequences.

How many sequences of 4 things can be formed from 9 different things with replacement and order is important?

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