Pascal 2023 Part B - Question 14, CEMC UWaterloo

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Difficulty: 3

This problem is tagged with pascal, pascal23, highschool.

(Pascal 2023, Part B, Question 14, CEMC - UWaterloo)

Each of four doors is randomly either open or closed. What is the probability that exactly two of the four doors are open?
$(A)$ $\frac{3}{8}$
$(B)$ $\frac{5}{16}$
$(C)$ $\frac{1}{4}$
$(D)$ $\frac{1}{2}$
$(E)$ $\frac{3}{16}$

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