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# At a certain university, 7 students from the 10-student history depart

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Math Expert
Joined: 02 Sep 2009
Posts: 46279
At a certain university, 7 students from the 10-student history depart [#permalink]

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08 Apr 2016, 02:51
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Difficulty:

35% (medium)

Question Stats:

77% (01:48) correct 23% (03:08) wrong based on 49 sessions

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At a certain university, 7 students from the 10-student history department and 5 students from the 7-student English department will be selected to form a 12-student committee. At a neighboring university, 2 students from a 10-person math department and 3 students from a 7-student science department will be selected to form a 5-student focus group. What is the ratio of the number of ways in which the 12-student committee can be formed to the number of ways in which the 5-student focus group can be formed?

A. 25/16
B. 8/5
C. 12/5
D. 16/5
E. 144/25

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Re: At a certain university, 7 students from the 10-student history depart [#permalink]

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08 Apr 2016, 21:21
Number of ways of selecting a 12 member student committee = 10C7 * 7C5
Number of ways of selecting a focus group of 5 students = 10C2 * 7C3

Ratio of 12 member student committee to 5 member focus group = $$\frac{10C7 * 7C5}{10C2 * 7C3}$$ = $$\frac{8}{5}$$

Intern
Joined: 18 May 2017
Posts: 12
Re: At a certain university, 7 students from the 10-student history depart [#permalink]

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21 May 2017, 08:40
Vyshak wrote:
Number of ways of selecting a 12 member student committee = 10C7 * 7C5
Number of ways of selecting a focus group of 5 students = 10C2 * 7C3

Ratio of 12 member student committee to 5 member focus group = $$\frac{10C7 * 7C5}{10C2 * 7C3}$$ = $$\frac{8}{5}$$

Would you kindly clarify how you canceled the combinations and got 8/5 at the end?
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Joined: 04 Jan 2016
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Re: At a certain university, 7 students from the 10-student history depart [#permalink]

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21 May 2017, 14:06
Michaelkalend13 wrote:
Vyshak wrote:
Number of ways of selecting a 12 member student committee = 10C7 * 7C5
Number of ways of selecting a focus group of 5 students = 10C2 * 7C3

Ratio of 12 member student committee to 5 member focus group = $$\frac{10C7 * 7C5}{10C2 * 7C3}$$ = $$\frac{8}{5}$$

Would you kindly clarify how you canceled the combinations and got 8/5 at the end?

It is going to be a long one, if you like it, don't forget to hit me with a kudos.

i) $$(\frac{10}{1}*\frac{9}{2}*\frac{8}{3}*\frac{7}{4}*\frac{6}{5}*\frac{5}{6}*\frac{4}{7})*(\frac{7}{1}*\frac{6}{2}*\frac{5}{3}*\frac{4}{4}*\frac{3}{5})=$$

ii) $$(\frac{10}{1}*\frac{9}{2})*(\frac{7}{1}*\frac{6}{2}*\frac{5}{3})=$$

Now, if you do the simplification and divide as $$\frac{i}{ii}$$ you will get $$\frac{8}{5}$$
Re: At a certain university, 7 students from the 10-student history depart   [#permalink] 21 May 2017, 14:06
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# At a certain university, 7 students from the 10-student history depart

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