MHB Find the probability that each group has an equal amount of odd and even numbers

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The discussion focuses on calculating the probability of specific outcomes when dividing a set of numbers from 1 to 4N into two equal groups. Participants seek to determine the likelihood that each group contains an equal number of odd and even numbers, as well as the distribution of numbers divisible by N. There is a request for clarification on the sequence of numbers, indicating a need for a more detailed explanation of the set. The conversation highlights the complexities involved in probability calculations related to group distributions. Overall, the thread emphasizes the importance of clear definitions in mathematical discussions.
Mehrudin
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A set of numbers 1,2,...,4N gets randomly divided into two groups with equal amount of numbers. Calculate the probability:7
a) Each group has an equal amount of odd and even numbers,
b) All numbers that are divisible by N, to fall in only one of the groups,
c) All numbers that are divisible by N, to be divided equally in the two groups.
 
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It's unclear, at least to me, what the sequence noted as 1, 2, ..., 4N is. You need to give a better description. What is intended?
 

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