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09 Oct 2019, 23:23
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
76% (02:50) correct
24%
(03:07)
wrong
based on 67
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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
A. 25/16
B. 8/5
C. 12/5
D. 16/5
E. 144/25
10 Oct 2019, 07:25
Kudos
Bookmarks
from given info
10c7*7c5/ 10c2*7c3 = 120*21/45/35 = 8/5
IMO B
10c7*7c5/ 10c2*7c3 = 120*21/45/35 = 8/5
IMO B
Bunuel
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
A. 25/16
B. 8/5
C. 12/5
D. 16/5
E. 144/25
13 Oct 2019, 18:16
Kudos
Bookmarks
Bunuel
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
A. 25/16
B. 8/5
C. 12/5
D. 16/5
E. 144/25
We can start with the first university:
10C7 = 10!/(7! x 3!) = (10 x 9 x 8)/(3 x 2) = 120
7C5 = 7!/(5! x 2!) = (7 x 6)/2 = 21
Thus, number of ways the 12-student committee can be formed at the first university is 120 x 21.
Now, for the second university:
10C2 = 10!/(8! x 2!) = (10 x 9)/2 = 45
7C3 = 7!/(4! x 3!) = (7 x 6 x 5)/(3 x 2) = 35
Thus, the number of ways the 5-student focus group can be formed at the second university is 45 x 35.
Therefore, the ratio is (120 x 21)/(45 x 35) = (15 x 8 x 3 x 7)/(15 x 3 x 5 x 7) = 8/5.
Answer: B
