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Home » Compute the third derivative \( p'''(x) \): - AMAZONAWS

Compute the third derivative \( p'''(x) \): - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Probabilidad:

📌 \frac{3\dbinom{17}{3} + \dbinom{16}{3} + 17 \times 17 \times 16}{\dbinom{50}{3}} = \frac{3 \times 680 + 560 + 4568}{19600} = \frac{2040 + 560 + 4568}{19600} = \frac{6168}{19600} = \boxed{\dfrac{1542}{4900}}

📌 Pregunta: ¿De cuántas maneras pueden sentarse 5 miembros distinguibles y 3 no miembros distinguibles alrededor de una mesa circular si se consideran equivalentes las rotaciones y las reflexiones?

📌 Solución: Para arreglos en círculo con reflexión, fijo un miembro para eliminar simetrías rotacionales y de reflexión. Los 4 miembros restantes se pueden arreglar de \(4!\) maneras, y los 3 no miembros de \(3!\) maneras. Total de arreglos:

📌 4! \times 3! = 24 \times 6 = \boxed{144}

📌 Pregunta: Calcula \(\dbinom{12}{5} - \dbinom{12}{4}\).

📌 Solución: Usando las propiedades de los coeficientes binomiales:

📌 \dbinom{12}{5} = \dbinom{12}{7}, \quad \dbinom{12}{4} = \dbinom{12}{8}

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Calculate each term separately:
2(2)^3 = 2 \times 8 = 16
-5(2)^2 = -5 \times 4 = -20
3(2) = 6
Combine these results with the constant term:
f(2) = 16 - 20 + 6 - 1 = 1
Thus, \(f(2) = \boxed{1}\).
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