I am doing Stat110 and in the book, "Introduction to Probability" they give the following definition of sampling with replacement:
Theorem 1.4.5 (Sampling with replacement). Consider n objects and making k choices from them, one at a time with replacement (i.e., choosing a certain object does not preclude it from being chosen again). Then there are n^k possible outcomes.
I tried to use the above definition to find out the number of outcomes (sample size) in a roll of two fair 6-sided dice and 12 fair 6-sided dice. I know the answer is 36 in one case and 6^12 in the other but I cannot really understand how to use the above theorem to get this number.
For example, if I have two 6-sided dice then n = 2 and each die has 6 choices. So should it not be 2^6?