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To graduate John needs to complete eight courses. Of these

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To graduate John needs to complete eight courses. Of these [#permalink] New post 22 Oct 2017, 06:13
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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


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[Reveal] Spoiler: OA
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Re: To graduate John needs to complete eight courses. Of these [#permalink] New post 22 Oct 2017, 09:16
John has to choose 8 courses and the he has a fixed amount of courses to take, i.e. 3 out of 5 science courses, 2 out of 6 math courses and 1 out of 4 history courses. Then, the 2 courses left can be whatever out of 20-15 = 5 remaining courses.

Thus, its combinations are \(5*4*3* *6*5* *4* *5*4 = 144,000\). However, since the order in which courses are taken does not matter, we have to divide it by 3!, 2!, 1! and 2! so that we get \(\frac{144,000}{3!*2!*1!*2!} = 6000\).

Answer D
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Re: To graduate John needs to complete eight courses. Of these [#permalink] New post 24 Oct 2017, 12:35
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5C3 * 6C2 * 4C1 * 5C2 = 6000.

Please note that 5C2 is taking 2 out of left 5 courses.
Re: To graduate John needs to complete eight courses. Of these   [#permalink] 24 Oct 2017, 12:35
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