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Home » حوّل اللترات إلى ملليلتر: 0.24 لتر * 1000 = 240 ملليلتر. - go-checkin.com

حوّل اللترات إلى ملليلتر: 0.24 لتر * 1000 = 240 ملليلتر. - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Mistake: formula \(\binom{n-k+1}{k}\) is for placing \(k\) non-adjacent indistinct items? No — standard formula for number of binary strings of length \(n\) with no two consecutive 1’s is \(F_{n+2}\), where \(F_1=1, F_2=1, F_3=2, F_4=3, F_5=5, F_6=8, F_7=13, F_8=21\)

📌 So \(F_{5+2} = F_7 = 13\) — matches.

📌 Thus, number of valid assignments is 13.

📌 But wait — no: \(F_{n+2}\) gives the count for \(k=1\) to \(k=\lfloor (n+1)/2 \rfloor\), but we want **exactly 4 H’s**? No — the problem does not fix number of H’s. It allows any number, as long as no two are adjacent.

📌 So total valid assignments: 13, as above.

📌 But earlier calculation with recurrence gave \(a_5 = 13\), yes.

📌 But let's verify with inclusion.

📌 Alternatively: number of binary strings of length 5 with no two consecutive 1’s is indeed 13.

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