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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? 📰 How Many Calories 1 Tablespoon Sugar 1528095 📰 Oculus Meta Quest 2 📰 Best Budget Jet Wash 2079000 📰 Connections Bints 160757 📰 Cubs Prediction 338737 📰 From Mysterious Strangers To Grizzled Outlaws Uncover The Hottest Rdr2 Characters Now 6104669 📰 Quantum Efficiency 1443669 📰 Free Samsung Galaxy Phones 📰 75 Inch Tv Black Friday 7802715 📰 Breaking Optx Stock Soars Over 200Heres Why You Need To Act Now 2102051 📰 Step Into The Madness Crazy Flips In 3D That Will Leave You Speechless 5351696 📰 Per Annum Meaning 3373452 📰 Reliable Rx Why This Pharmacy Service Gets Top Reviews Never Throws You Off 82442 📰 Youtube Music Playlists 165693 📰 Ternen Cill The Truth No One Dares Reveal Beneath The Facing Sky 5481786