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16 Sep 2014, 01:00
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If out of 200 programmers, 30% are familiar with Python, 80% with JavaScript, and 10% do not have proficiency in either of these programming languages, how many ways can a team of three programmers, all proficient in both Python and JavaScript, be formed?
A. 2960
B. 3990
C. 6840
D. 8820
E. 9880
A. 2960
B. 3990
C. 6840
D. 8820
E. 9880
16 Sep 2014, 01:00
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Official Solution:
If out of 200 programmers, 30% are familiar with Python, 80% with JavaScript, and 10% do not have proficiency in either of these programming languages, how many ways can a team of three programmers, all proficient in both Python and JavaScript, be formed?
A. 2960
B. 3990
C. 6840
D. 8820
E. 9880
Total = Python + JavaScript - Both + Neither.
• If 30% are familiar with Python, then Python \(= 0.3*200 = 60\).
• If 80% are familiar with JavaScript, then JavaScript \(= 0.8*200 = 160\).
• If 10% are not proficient in either language, then Neither \(= 0.1*200 = 20\).
Substituting these values into the equation, we get \(200 = 60 + 160 - Both + 20\), which implies Both \(= 40\).
The number of different teams of 3 that can be formed from these 40 programmers is given by \(C^3_{40} = \frac{40!}{3!*37!} = \frac{38*39*40}{2*3} = 19*13*40 = 9880\).
Answer: E
If out of 200 programmers, 30% are familiar with Python, 80% with JavaScript, and 10% do not have proficiency in either of these programming languages, how many ways can a team of three programmers, all proficient in both Python and JavaScript, be formed?
A. 2960
B. 3990
C. 6840
D. 8820
E. 9880
Total = Python + JavaScript - Both + Neither.
• If 30% are familiar with Python, then Python \(= 0.3*200 = 60\).
• If 80% are familiar with JavaScript, then JavaScript \(= 0.8*200 = 160\).
• If 10% are not proficient in either language, then Neither \(= 0.1*200 = 20\).
Substituting these values into the equation, we get \(200 = 60 + 160 - Both + 20\), which implies Both \(= 40\).
The number of different teams of 3 that can be formed from these 40 programmers is given by \(C^3_{40} = \frac{40!}{3!*37!} = \frac{38*39*40}{2*3} = 19*13*40 = 9880\).
Answer: E
20 Oct 2023, 00:55
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
