Final answer:
The chance of selecting Tommy, Ted, and Peter in a systematic random sample of size 3 is 1 in (N/3), where N is the population size.
Explanation:
In a systematic random sampling method, every kth element is selected from a population of size N after a random start. Given a sample size of 3, the probability of selecting Tommy, Ted, and Peter in that specific order is 1 in (N/3). This is because each has an equal chance of being the starting point (1 in 3), and subsequently, a 1 in 3 chance of being picked for each subsequent slot in the sample. Therefore, considering the permutations of individuals within a sample of size 3, the overall likelihood becomes 1 in (N/3). This assumes an unbiased systematic random sampling method where each individual has an equal chance of being chosen at any given position within the sample.
In summary, the likelihood of the specific sequence of Tommy, Ted, and Peter being chosen in a systematic random sample of size 3 is 1 in (N/3), accounting for the equal probability of each individual being selected at any position within the sample.
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