1. The problem asks how the denominator in the probability calculation changes when drawing two marbles one after the other without replacement. 2. When drawing marbles without replacement, the total number of marbles decreases after the first draw. 3. Initially, if there are $N$ marbles, the probability of drawing the first marble is $\frac{1}{N}$. 4. After drawing one marble, there are now $N-1$ marbles left, so the denominator for the second draw changes to $N-1$. 5. This is because the sample space shrinks by one after the first marble is removed, affecting the probability of the second draw. 6. Therefore, the denominator changes from $N$ to $N-1$ to reflect the reduced total number of marbles available for the second draw.