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How many sequences of 5 things can be formed

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Suppose a sample 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, ca, cb, cc}.

Now suppose there are Y different things. There are Y ways the first draw can occur. For each of the Y way the first draw can occur, there are Y ways the second 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 26x26x26x10x10x10= 26 * 10 = 17,576,000. From this one style of plates, there are many sequences.

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

Reference no: EM132474215

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