Cayley 2023 Part A - Question 10, CEMC UWaterloo

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This problem is tagged with cayley, cayley23, highschool.

(Cayley 2023, Part A, Question 10, CEMC - UWaterloo)

Each of five doors is randomly either open or closed. What is the probability that exactly two of the five doors are open?
$(A)$ $\frac{5}{16}$
$(B)$ $\frac{13}{32}$
$(C)$ $\frac{9}{25}$
$(D)$ $\frac{1}{2}$
$(E)$ $\frac{7}{16}$

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