Final answer:
The question asks the number of spins required to land on each of the 8 options in a spinner, where repeats are allowed. However, none of the answers provided directly answer the question correctly based on the coupon collector's problem. Despite this, the question requires knowledge of combinatorics and expected value in Mathematics.
Step-by-step explanation:
The student's question pertains to the theoretical number of spins required to land on all 8 options on a spinner with 8 different options, where repeats are allowed. This question can be analyzed using the concept of probability and combinatorics in Mathematics. Since the spinner is fair, each spin is independent, and the probability of landing on a particular option is the same for every spin. The number of spins required to land on all options at least once does not have a simple formula and involves the mathematical concepts of expected value and the coupon collector's problem.
However, the specific question seems to be asking for an answer that is not factually correct as none of the provided options directly relate to the coupon collector's problem. The average number of spins to collect all options could be obtained using the harmonic series and is higher than any of the given choices. Therefore, none of the options (a. 8 b. 16 c. 24 d. 56) accurately represents the expected number of spins based on the problem as it's typically understood.