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, there are Y ways the second draw can occur, resulting in Y times Y, or

Y

sequences. For each of the Y

sequences formed from 2 draws, there are Y ways the 3rd draw can

2

2

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 26

x 26 x 26 x 10 x 10 x 10 = 26

3

x 10

3

= 17,576,000. From this one style of plate, there are many sequences.

How many sequences of 3 things can be formed from 7 different things with replacement and order is

important?