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?

480

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

To find the total number of ways the college freshman can arrange his or her program for the first term, we need to multiply the number of choices for each course category.

Science courses: There are 6 options.
Humanities courses: There are 4 options.
Elective courses: There are 5 options.
Mathematics courses: There are 4 options.

To calculate the total number of ways, we multiply these numbers together:

Total number of ways = (Number of science courses) * (Number of humanities courses) * (Number of elective courses) * (Number of mathematics courses)
Total number of ways = 6 * 4 * 5 * 4
Total number of ways = 480

Therefore, the college freshman can arrange his or her program in 480 different ways for the first term.

To find the total number of ways the college freshman can arrange their program for the first term, we need to multiply the number of options for each subject.

Number of science courses: 6
Number of humanities courses: 4
Number of elective courses: 5
Number of mathematics courses: 4

To calculate the total number of ways, we multiply these numbers together:

6 (science courses) x 4 (humanities courses) x 5 (elective courses) x 4 (mathematics courses) = 480

Therefore, the college freshman can arrange their program in 480 different ways for the first term.