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# To graduate John needs to complete eight courses. Of these

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Senior Manager
Joined: 20 May 2014
Posts: 282
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Kudos [?]: 50 [0], given: 220

To graduate John needs to complete eight courses. Of these [#permalink]  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

Kudos for correct solution.
[Reveal] Spoiler: OA
Director
Joined: 03 Sep 2017
Posts: 521
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Kudos [?]: 344 [0], given: 66

Re: To graduate John needs to complete eight courses. Of these [#permalink]  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 $$\frac{144,000}{3!*2!*1!*2!} = 6000$$.

Manager
Joined: 01 Apr 2017
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WE: Analyst (Computer Software)
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Kudos [?]: 62 [1] , given: 27

Re: To graduate John needs to complete eight courses. Of these [#permalink]  24 Oct 2017, 12:35
1
KUDOS
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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# To graduate John needs to complete eight courses. Of these

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