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Home » 3er término: \( 15 \times 3 = 45 \) - Network4

3er término: \( 15 \times 3 = 45 \) - Network4

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 In a lab experiment, a scientist uses a machine that emits one of six different colored light pulses (red, orange, yellow, green, blue, violet), each equally likely. If the machine is activated three times independently, what is the probability that all three pulses are different colors?

📌 The machine emits one of six colors uniformly at random on each activation, independently.

📌 Number of favorable outcomes where all three colors are different:

📌 A community board meeting consists of 5 environmental scientists and 3 local residents. If they sit around a circular table, with all individuals distinguishable, how many distinct seating arrangements are possible such that no two residents sit next to each other?

📌 We fix one persons position to account for rotational symmetry in circular arrangements. Lets fix one scientist at a seat.

📌 Once all scientists are seated, there are 5 gaps between them (one between each adjacent pair) where residents can be placed. We must choose 3 of these 5 gaps to place one resident each, ensuring no two residents are adjacent.

📌 Total number of ways to choose 5 distinct numbers from 20:

📌 How many 8-digit positive integers consist only of the digits 1 and 3, and contain at least one pair of consecutive 1s?

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4x - 7 = 9
4x = 16
Divide both sides by 4:
Thus, the value of $x$ that satisfies the equation is:
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