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To graduate John needs to complete eight courses. Of these eight, he

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Math Expert
Joined: 02 Sep 2009
Posts: 54369
To graduate John needs to complete eight courses. Of these eight, he  [#permalink]

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31 Jul 2017, 23:55
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Difficulty:

55% (hard)

Question Stats:

58% (02:44) correct 42% (02:21) wrong based on 54 sessions

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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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Re: To graduate John needs to complete eight courses. Of these eight, he  [#permalink]

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01 Aug 2017, 00:07
Bunuel wrote:
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

5C3 (Science) * 6C2 (Math) * 4C1 (History) * 5C2 (Other 20-5-6-4 =5; 8-3-2-1 =2) = 10* 15 * 4 * 10 = 6000

D
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Re: To graduate John needs to complete eight courses. Of these eight, he  [#permalink]

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01 Aug 2017, 21:51
Here is what the scenario is:
John requires to chose:
* 3 Science Classes out of 5 science classes on offer.
* 2 Maths Classes out of 6 Maths classes on offer.
* 1 History Class out of 4 History classes on offer.
* 2 remaining classes out 5 other subjects classes on offer.
Total combinations possible are,
5C3 + 6C2 + 4C1 + 5C2 = 6000 which is option D.
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Re: To graduate John needs to complete eight courses. Of these eight, he   [#permalink] 01 Aug 2017, 21:51
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