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📰 Solution: The total number of possible state combinations is $2^5 = 32$. The number of ways to choose 2 elements to be active is $\binom{5}{2} = 10$. Since each combination is equally likely, the probability is $\frac{10}{32} = \frac{5}{16}$. Thus, the final answer is $\boxed{\dfrac{5}{16}}$. 📰 Question: A mechanical engineer tests 6 nanoscale sensors, each with 3 calibration settings. What is the probability that exactly 4 sensors are set to "precision mode" if each setting is chosen uniformly and independently? 📰 Solution: The total number of possible calibration configurations is $3^6$. To count favorable cases, choose 4 sensors to be in "precision mode" in $\binom{6}{4}$ ways, and the remaining 2 sensors can be in either of the other 2 settings, giving $2^2$ possibilities. The probability is $\frac{\binom{6}{4} \cdot 2^2}{3^6} = \frac{15 \cdot 4}{729} = \frac{60}{729} = \frac{20}{243}$. Thus, the final answer is $\boxed{\dfrac{20}{243}}$.Question: A tech startup founder wants to align two project timelines with cycles of 10 and 15 months. What is the least number of months after which both projects will synchronize? 📰 Characters In Winx 📰 Public Reaction Poetry Vs Uv And Nobody Expected 📰 Verizon Tomahawk Wi 📰 Adam Levine Maroon 5 Net Worth 5206217 📰 Game Apps For Free 161551 📰 Discover The Hidden Strength Of The Silver Guardian Protect Defend Conquer 5472388 📰 Celanese Stock 5985081 📰 Stock Frontier 📰 Factory Mapping 📰 Health Catalyst 9400881 📰 Investment For Beginners 📰 Auto Insurance List Of Companies 📰 Highest Money Market Account 8202768 📰 Stock Anet The Hidden Giants Generating 1M Monthly Dont Miss This Financial Goldmine 6484642 📰 Critical Evidence Reliance India Limited Share Price And It S Alarming