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Different things with replacement and order is important

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Suppose a sampling space has things a, b, and c. Twice draw from the sample space and replace. The possible sequence formed are {aa,ab,ac,ba,bb,bc,cacb,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 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.

How many sequence of 5 things can be formed from 7 different things with replacement and order is important?

Reference no: EM132150383

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