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Could you explain why divided by 4? Also if it is a circle wouldn't your 2 outcomes be the same? They would not look different around a circle as opposed to a straight line. The provided solutions did: M1. 2x3!x4! = 288I have a feeling I may be wrong. Someone correct me if so.
Pretend that F represents a pair of females and M represents a pair of males.
Consider a straight line arrangement. We can have either
M F M F
or
F M F M
There are 2 outcomes.
Now, effectively the 4 men have 4 different places they can go. (e.g. f f _ _ f f _ _ )
4! possible outcomes.
Similarly, so can the women. 4! possible outcomes.
Hence, in a straight line formation the answer is 2(4!)(4!) = 576
But we are talking about a circular arrangement, where there is no start. We need to cater for this by dividing by 4.
Hence 2(4!)(4!)/4 = 288
Call the males A, B, C, D. Note in the table's arrangement, it'll be:Could you explain why divided by 4? Also if it is a circle wouldn't your 2 outcomes be the same? They would not look different around a circle as opposed to a straight line. The provided solutions did: M1. 2x3!x4! = 288
M2. 4C2/2! x 2! x 4! = 288
M3. 3 x 2! x 2! x 4! = 288