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Home » You Won’t Believe What Happened When We Restored Last-Gen Wii U Gameplay! - Leaselab

You Won’t Believe What Happened When We Restored Last-Gen Wii U Gameplay! - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 We compute $ S(6,2) = 2 \cdot S(5,2) + S(5,1) = 2 \cdot 15 + 1 = 31 $, or known $ S(6,2) = 31 $. Then:

📌 S(7,3) = 3 \cdot 90 + 31 = 270 + 31 = 301.

📌 Thus, the number of ways to partition the 7 distinct artifacts into 3 indistinguishable non-empty containers is $ \boxed{301} $.

📌 Question: A science educator is designing a virtual lab where students simulate flipping 6 fair coins and rolling a single 6-sided die. What is the probability that the number of heads equals the value rolled on the die?

📌 Solution: Let $ H $ be the number of heads in 6 flips of a fair coin, so $ H \sim \text{Binomial}(6, \frac{1}{2}) $. Let $ D $ be the outcome of a fair 6-sided die, uniformly distributed over $ \{1,2,3,4,5,6\} $. We seek $ P(H = D) $.

📌 Since $ D $ takes integer values from 1 to 6, we only consider values of $ H = k $ for $ k = 1,2,3,4,5,6 $. But $ H $ max is 6, so all values are possible.

📌 Because $ D $ and $ H $ are independent:

📌 P(H = D) = \sum_{k=1}^{6} P(H = k) \cdot P(D = k) = \sum_{k=1}^{6} \binom{6}{k} \left(\frac{1}{2}\right)^6 \cdot \frac{1}{6}.

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لتكن \( x \) عدد المكاتب و \( y \) عدد الطاولات.
\( x + y = 30 \)
\( 120x + 180y = 7800 \)
بحل هاتين المعادلتين، استبدل \( y = 30 - x \) في المعادلة الثانية:

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