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Ssuppose a sample space has things a,b,c. Twice, draw from the sample s

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Ssuppose a sample space has things a,b,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 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 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 sequences of 5 things can be formed from 7 Different things with replacement and order is important?

 
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