To graduate, John needs to complete eight courses. Of these eight, he must take only three science courses, only two...

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To graduate, John needs to complete eight courses. Of these eight, he must take only three science courses, only two math courses, and only one history course. If the college offers five science courses, six math courses, and four history courses, how many different class schedules can John have if the college offers a total of twenty courses?

A. 150
B. 600
C. 3000
D. 6000
E. 12450

OA D

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He needs to take 8 courses in total, with 3+2+1=6 from the stated curriculum, leaving 2 other courses to be taken outside the stated curriculum.

There are 5+6+4=15 courses available from the stated curriculum and 20 courses in total. So the 2 courses to be taken outside the curriculum can be selected in 5!/2!3!= 10 ways.

The 3 science courses can be selected from the 5 available 5!/2!3!= 10 ways

The 2 math courses selected from 6 available 6!/2!4!=15 ways

The 1 history course from the 4 available 4!/3!1!= 4 ways

Total ways = 10*10*15*4=6000,D