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Home » Total: $ 3 \cdot 2^4 = 48 $ - Get link 4share

Total: $ 3 \cdot 2^4 = 48 $ - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 \frac{6}{66} = \frac{1}{11}

📌 The probability that both selected zones are in the same work area is $\boxed{\frac{1}{11}}$.

📌 Question: A digital health system uses a 5-character verification code composed of uppercase letters (A–Z) and digits (0–9), where the first character must be a letter, and no character is repeated. How many valid verification codes are possible?

📌 Solution: The code starts with a letter, so there are 26 choices for the first character. For the remaining 4 characters, we choose from the remaining $25 + 10 = 35$ characters (since one letter has already been used), with no repetition:

📌 \times P(35, 4) = 26 \times \frac{35!}{(35 - 4)!} = 26 \times \frac{35!}{31!}

📌 \times 34 \times 33 \times 32 = 125Point6120

📌 \times 1256120 = 32665920

📌 Thus, the total number of valid verification codes is $\boxed{32665920}$.

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P(k \text{ éxitos en } n \text{ ensayos}) = \binom{n}{k} p^k (1-p)^{n-...
Aquí, \( n = 4 \), \( k = 2 \), \( p = \frac{1}{6} \), y \( 1 - p = \f...
P(2 \text{ cuatros en } 4 \text{ lanzamientos}) = \binom{4}{2} \left(\...
Primero, calculamos el coeficiente binomial:
\binom{4}{2} = \frac{4!}{2!2!} = 6
A continuación, calculamos las probabilidades:
\left(\frac{1}{6}\right)^2 = \frac{1}{36}, \quad \left(\frac{5}{6}\rig...
Multiplicamos estos juntos:
\times \frac{1}{36} \times \frac{25}{36} = \frac{150}{1296} = \frac{25...
Por lo tanto, la probabilidad es:

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