Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

00:00

Question Stats:

100% (00:27) correct
0% (00:00) wrong based on 1 sessions

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?

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 \(\frac{144,000}{3!*2!*1!*2!} = 6000\).