Question 10, 11.2.47 At a benefit concert, nine bands have volunteered to perform but there is only enough time for six of the bands to play. How many lineups are possible?

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

In a group of people on holiday, it is established that there are: - 10 males under the age of 21 - 8 females under the age of 21 - 6 males aged between 21 and 30 - 5 females aged between 21 and 30 Calculate the probability that, if one person is selected at random from the group this person will be: \( \begin{array}{ll}\text { a) A male under the age of } 30 . \\ \text { b) A female. } \\ \text { c) A male over the age of } 21 . \\ \text { d) A person not older than } 21 . \\ \text { e) A male given that this person is over } 30 \text { years. } \\ \text { f) A female or between } 21 \text { and } 30 . \\ \text { g) A male or a female. }\end{array} \)

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?

1. Según estadísticas la probabilidad de que el motor de un auto nuevo de cierta marca sufra algún desperfecto en el primer año de uso es de 0.02 , si se prueban tres automóviles de esta marca, encuentre el número esperado de autos que no sufren de algún desperfecto en el primer año y su desviación estándar. Resultados \( \mu=2.94 \) y \( \sigma=0.2425 \)

3. La probabilidad de que cierta clase de componente sobreviva a una prueba de choque es de 0.85. De los siguientes 15 componentes que se prueban calcule la probabilidad de que: a). sobrevivan 10 componentes. \( R=0.04489 \) b). no sobrevivan máximo 2 componentes. \( R=0.6042 \) c) calcule el promedio de componentes que sobreviven. \( R=12.75 \)