77. En cierta población el \( 30 \% \) de los habitantes se encuentran afectados por un virus, la segunda semana el \( 10 \% \) de los enfermos se recupera y el \( 30 \% \) de los sanos se contagia. En la segunda semana, al escoger 5 personas al azar, źcuál es la probabilidad que dos de ellas estén enfermas? A) \( \left(\frac{21}{100}\right)^{2} \cdot\left(\frac{49}{100}\right)^{3} \) B) \( \left(\frac{52}{100}\right)^{2} \cdot\left(\frac{48}{100}\right)^{3} \) C) \( 10 \cdot\left(\frac{21}{100}\right)^{2} \cdot\left(\frac{49}{100}\right)^{3} \) D) \( 10 \cdot\left(\frac{52}{100}\right)^{2} \cdot\left(\frac{48}{100}\right)^{3} \) E) \( 10 \cdot\left(\frac{52}{100}\right)^{3} \cdot\left(\frac{48}{100}\right)^{2} \)

A club with fifteen members is to choose three officers: president, vice-president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?

\begin{tabular}{l} Fundamental \\ \( K \quad \) An ice cream store sells 2 drinks, in 5 sizes, and 4 flavors. In how many ways can a customer order a drink? \( 0 \%, 0 \) of 5 points \\ \hline\end{tabular}

\( 1 \leftarrow \quad \begin{array}{l}\text { In a race in which five automobiles are entered and there are no ties, in how many ways can the } \\ \text { first three finishers come in? }\end{array} \)

Question A small ice cream shop conducted a survey asking customers what their number one favorite flavor of ice cream is. The results showed that 51 favor vanilla, 14 fayor strawbery, 60 favor chocolate, and 11 favor other flavors. What is the probability that a randomly selected customer favors either vanila or strawberry? Enter your answer as a simplified fraction.

In how many ways can the digits in the number \( 7,441,111 \) be arranged?