Question

A college freshman must take a science course, a humanities course, an elective course, and a mathematics course for the first term of the school year. If he or she may select any of the six science courses, any of the four humanities courses, any of the five elective courses, and any of the four mathematics courses which are all open for enrollment, in how many ways can he or she arrange his or her program for the first term?

Answer 1

She can choose her courses in 6*4*5*4 ways.

For each of the sets of 4 courses, she can arrange her schedule in 4! ways.

so, 6*6*5*4*24

Answer 2

480