Assuming we have a Set of N elements and we form samples of size N by sampling with replacement the original Set, how many such samples can we construct?
Alternatively, the question is: How many combinations of size N exist of N elements, when each element can be used more than once in a combination?
Your advice will be appreciated.
You have $N $ choices each of $N $ different times. The choices are independent, so you multiply the number of possibilities, to get