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26 May 2016, 11:49
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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74% (02:30) correct
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In a certain group of 10 developers, 4 developers code only in Python and the rest program in either Ruby on Rails or PHP - but not both. If a developer organization is to choose a 3-member team, which must have at least 1 developer who codes in Python, how many different programming teams can be chosen?
(A) 100
(B) 40
(C) 66
(D) 80
(E) 75
(A) 100
(B) 40
(C) 66
(D) 80
(E) 75
26 May 2016, 20:09
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Bunuel
In a certain group of 10 developers, 4 developers code only in Python and the rest program in either Ruby on Rails or PHP - but not both. If a developer organization is to choose a 3-member team, which must have at least 1 developer who codes in Python, how many different programming teams can be chosen?
(A) 100
(B) 40
(C) 66
(D) 80
(E) 75
(A) 100
(B) 40
(C) 66
(D) 80
(E) 75
Two ways...
1) total ways = 10C3 = 10!/7!3! = 120..
ways without python developer = 6C3= 6!/3!3!=20..
ways of atleast ONE python developer = 120-20 =100..
2) ways of selecting ONLY one = 4*6C2 = 4*15 = 60..
ways of selecting ONLY two = 4C2*6C1 = 6*6 = 36..
ways of selecting all three = 4C3 = 4 = 4..
Total = 60+36+4=100...
General Discussion
27 May 2016, 01:52
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There are 4 python developers.
Whenever there is a case of "at least one is to be chosen", it is always better to use (Total - When none is chosen)
When there are no restrictions, we can select 3 members out of 10 people, in 10C3 ways: This works out to 120.
Now when we have to select 3 persons out of 10 persons such that NONE of them is a Python developer, then, this is as good as selecting 3 persons out of 6 persons (leave out all 4 python developers). This can be done in 6C3 ways = 20 ways.
120-20 = 100 ways. These are the different ways in which we can choose a team such that at least one Python developer is included.
Whenever there is a case of "at least one is to be chosen", it is always better to use (Total - When none is chosen)
When there are no restrictions, we can select 3 members out of 10 people, in 10C3 ways: This works out to 120.
Now when we have to select 3 persons out of 10 persons such that NONE of them is a Python developer, then, this is as good as selecting 3 persons out of 6 persons (leave out all 4 python developers). This can be done in 6C3 ways = 20 ways.
120-20 = 100 ways. These are the different ways in which we can choose a team such that at least one Python developer is included.
