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Bunuel
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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

Number of 3-member programming teams that can be formed in which at least one member of the group codes in Python = Total Number of different teams of 3 that can be formed - Number of different teams of 3 that can be formed in which no member of the group codes in Python
Total Number of different teams of 3 that can be formed = 10!/7!3! = 120
Number of different teams of 3 that can be formed in which no member of the group codes in Python = 6!/3!3! = 20
Number of different teams of 3 that can be formed in which at least one member of the group codes in Python = 120 - 20 = 100
Answer - A
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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

We can use the formula:

Number of ways to select at least 1 developer who codes in Python = total number of ways - Number of ways to select no developers who code in Python

Total number of ways to select the group:

10C3 = 10!/[3! (10-3)!] = 10!/[3! 7!] = (10 x 9 x 8)/(3!) = (10 x 9 x 8)/(3 x 2 x 1) = 10 x 3 x 4 = 120 ways

Total number of ways to select no developers who code in Python:

6C3 = 6!/[3! (6-3)!](6 x 5 x 4)/(3!) = (6 x 5 x 4)/(3 x 2 x 1) = 20

Number of ways to select at least 1 developer who codes in Python = 120 - 20 = 100

Answer: A
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