Problem 2 - Entrance Test

The problem states that 5 people must be seated in a row with each person seated next to someone of the opposite gender. Given the constraint, we realize there must be an even number of people to alternate genders, but since we only have 5 people, they cannot be strictly alternated by gender. However, since the problem seems to be constructed with an assumption or oversight regarding an odd number of total people, let's reassess with a possible understanding that there are indeed more than one person of each gender, meaning there are both men and women but with a total of 5 people, implying either 3 of one gender and 2 of the other (or vice versa), and we want to maximize alternation under the constraint. If we have 3 of one gender (let's say women) and 2 of the other (men), the arrangement could look like MWMWM, which satisfies the condition given. To calculate the number of arrangements: for the MWMWM arrangement, the 3 women can be arranged in 3! ways, and the 2 men can be arranged in 2! ways. Thus, the number of ways is 3! * 2! = 12. However, the arrangement could also start with a woman (W), leading to a WMWMW pattern, which is essentially the same as the MWMWM pattern when considering circular permutations aren't mentioned and starting point doesn't change the relative positioning, so these are not distinct in the context provided. The actual distinct question should involve counting these arrangements directly under the given conditions. So, for either arrangement pattern (starting with a man or a woman), considering the specific pattern required, the calculation provided earlier stands as the method to find arrangements under the constraints given, but we must match the answer format. Since this calculation doesn't align perfectly with the provided choices and involves an understanding that doesn't perfectly match the initial AMC-style simplicity, we recognize an error in aligning the problem's conditions with the expected answer format. However, sticking strictly to given formats and the problem as closely as interpreted, we might align with a basic principle of such arrangement questions.