Reference no: EM133010897
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. 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(squared) sequences. For each of the Y (squared) sequences formed from 2 draws, there are Y ways the 3rd draw can occurred forming Y times Y times Y or Y (cubed) sequences. Generalizing there are Y(exponent x) sequences formed by drawing X time from Y different things with replacement.
Example: The number of state license plates that can be made with 3 letters followed by 3 numbers in 26x26x26x10x10x10 = 26(cubed)x10(cubed) = 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?