MathDB

For the Dürer final results announcement, four loudspeakers are used to provide sound in the hall. However, there are only two sockets in the wall from which the power comes. To solve the problem, Ádám got two extension cords and two power strips. One plug can be plugged into an extension cord, and two plugs can be plugged into a power strip. Gábor, in his haste before the announcement of the results, quickly plugs the

8

plugs into the

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holes. Every possible way of plugging has the same probability, and it is also possible for Gábor to plug something into itself. What is the probability that all

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speakers will have sound at the results announcement? For the solution, give the sum of the numerator and the denominator in the simplified form of the probability. A speaker sounds when it is plugged directly or indirectly into the wall.

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Problems(2)