Final answer:
The question contains a typo, but the correct approach to determine the number of different outcomes when drawing 8 cards from a deck with replacement is to calculate 52 to the power of 8. None of the provided answer options match this calculation.
Step-by-step explanation:
The question asks us to determine the number of different outcomes possible when drawing 8 cards from a deck with replacement. To solve the mathematical problem completely, we must understand the concept of sampling with replacement. In this scenario, each draw is an independent event, meaning the card is returned to the deck and can be drawn again.
With a standard deck of 52 cards, every draw has 52 potential outcomes since any card can be drawn at each step. To find the total number of possible outcomes for 8 draws, we calculate 52 to the power of 8 (528). This calculation gives us the number of different sequences or combinations of cards that can be drawn in 8 tries with replacement. However, the actual calculation of 528 is not presented in the answer options, indicating that the information given with the question has a typo in the hint stating '52 to the power of 5'. The correct calculation for 8 draws should indeed be 528, which is a much larger number than any of the options provided (a) 64, (b) 128, (c) 256, (d) 512. Therefore, none of the provided options are correct.
If we correct the typo and assume it meant to say '52 to the power of 3', the answer would be 523, as an example of how to approach the problem. However, since the question specifically asks for 8 draws, this corrected example does not provide the solution to the original question.