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16 May 2019, 00:13
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
74% (02:31) correct
26%
(02:32)
wrong
based on 217
sessions
History
Date
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A film production company must submit 5 of its movies released this year for consideration for an awards ceremony. This year, the company released 14 movies; 8 of these were horror movies and 6 were romantic comedies. If it submits at least 3 romantic comedies, how many groups of 5 movies can be submitted?
A. 276
B. 432
C. 560
D. 681
E. 686
A. 276
B. 432
C. 560
D. 681
E. 686
16 May 2019, 02:43
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Bunuel
A film production company must submit 5 of its movies released this year for consideration for an awards ceremony. This year, the company released 14 movies; 8 of these were horror movies and 6 were romantic comedies. If it submits at least 3 romantic comedies, how many groups of 5 movies can be submitted?
A. 276
B. 432
C. 560
D. 681
E. 686
A. 276
B. 432
C. 560
D. 681
E. 686
total combination possible
6c3*8c2+6c4*8c1+6c5
560+120+6
IMO E ; 686
16 May 2019, 05:28
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This is a question on applying the concepts of combinations, with added constraints on the selection. Note that the question says ‘at least 3 romantic comedies must be selected’. This means that there will be multiple cases and therefore, the values will have to be finally added.
We have a total of 8 horror movies and 6 rom coms. Of the 14,we have to select 5 movies such that at least 3 are rom coms. This means, we may select the movies in the following ways:
3 rom coms and 2 horror – This can be done in 6C3 * 8C2 ways, which is equal to 20 * 28 = 560 groups.
4 rom coms and 1 horror – This can be done in 6C4 * 8C1 ways, which is equal to 15* 8 = 120 groups.
5 rom coms and no horror – This can be done in 6C5 * 8C0, which is equal to 6 * 1 = 6 groups.
Therefore, this is a total of 686 groups.
So, the correct answer option is E.
Hope this helps!
We have a total of 8 horror movies and 6 rom coms. Of the 14,we have to select 5 movies such that at least 3 are rom coms. This means, we may select the movies in the following ways:
3 rom coms and 2 horror – This can be done in 6C3 * 8C2 ways, which is equal to 20 * 28 = 560 groups.
4 rom coms and 1 horror – This can be done in 6C4 * 8C1 ways, which is equal to 15* 8 = 120 groups.
5 rom coms and no horror – This can be done in 6C5 * 8C0, which is equal to 6 * 1 = 6 groups.
Therefore, this is a total of 686 groups.
So, the correct answer option is E.
Hope this helps!
