Two numbers are selected from the set {2, 4, 6, 8}. What is the difference in the number of possible outcomes if the experiment is undertaken with replacement or without replacement?

To answer this question, we first need to understand what it means to select numbers with replacement and without replacement.

1. With replacement means that after a number is selected, it is put back into the set before the next number is selected. This means that the same number can be selected more than once.

2. Without replacement means that once a number is selected, it is not put back into the set, so it cannot be selected again.

The set given is {2, 4, 6, 8}, which has 4 elements.

1. If we are selecting with replacement, then after we select the first number, there are still 4 numbers that we can select for the second number. So the total number of possible outcomes is 4*4 = 16.

2. If we are selecting without replacement, then after we select the first number, there are only 3 numbers left that we can select for the second number. So the total number of possible outcomes is 4*3 = 12.

So the difference in the number of possible outcomes if the experiment is undertaken with replacement or without replacement is 16 - 12 = 4.