Question

17. SCHEDULE At Randolph High School, there are

17 different classes offered to sophomores each semester. Four classes can be taken each semester
and students may not repeat a class during the year. What is the probability of the student taking English, History I,
Algebra and Spanish II the first semester and taking History II, Spanish III, Geometry and Biology the next semester?

Answer 1

Answer:To find the probability of the student taking English, History I, Algebra, and Spanish II in the first semester, and History II, Spanish III, Geometry, and Biology in the next semester, we need to calculate the probability of each event occurring and then multiply them together.

First Semester:

The student needs to choose 4 classes out of the 17 classes offered. So, the probability of choosing English, History I, Algebra, and Spanish II is:

P(English) * P(History I) * P(Algebra) * P(Spanish II) = 1/17 * 1/16 * 1/15 * 1/14

Second Semester:

Similarly, the student needs to choose 4 classes out of the remaining 13 classes offered (since one class has already been taken). So, the probability of choosing History II, Spanish III, Geometry, and Biology is:

P(History II) * P(Spanish III) * P(Geometry) * P(Biology) = 1/13 * 1/12 * 1/11 * 1/10

To find the overall probability, we multiply the probabilities from both semesters together:

P = (1/17 * 1/16 * 1/15 * 1/14) * (1/13 * 1/12 * 1/11 * 1/10)

Calculating this expression gives us the probability of the student following the specified schedule.

Explanation: