In a corporate company, eight engineers participate in a technical discussion with each other to design a product. Each one has to discuss with everyone else.How many discussions will they have to decide on the final design of that specific product?

1. A

   12

2. B

   28

3. C

   15

4. D

   21

Appeared in: ESIC Nursing Officer -2019 (Shift -1)

Explanation

• This problem requires calculating the number of unique pairs from a group of 8, where order does not matter.
• The formula to calculate the number of pairs (or handshakes/discussions) among 'n' items is n × (n - 1) / 2.
• Substituting n = 8 into the formula gives: 8 × (8 - 1) / 2.
• This simplifies to 8 × 7 / 2, which equals 56 / 2.
• The final result is 28, representing the total number of unique discussions.

Why Other Options Were Wrong

• Option A: The value 12 is incorrect. It might be a result of a miscalculation or using an incorrect formula.
• Option C: The value 15 is incorrect. This would be the correct answer if there were 6 engineers (6 × 5 / 2 = 15).
• Option D: The value 21 is incorrect. This would be the correct answer if there were 7 engineers (7 × 6 / 2 = 21).

Related Visual

• Visual 1: Infographic: A diagram showing 8 points (representing engineers) with lines connecting every pair of points, visually demonstrating the 28 unique connections.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Combinations and Permutations as background academic context rather than a clinical decision trigger.
• This question tests logical reasoning and mathematical aptitude, which are essential skills for problem-solving in any professional field, including healthcare management and resource allocation.
• While not a clinical question, the ability to perform systematic calculations is crucial for tasks like calculating drug dosages, staffing ratios, or interpreting statistical data in research.
• What if the question stated that discussions happen in a structured chain (Engineer 1 talks to 2, 2 talks to 3, etc., and 8 talks back to 1)? The answer would be 8, as there would only be 8 discussions in that specific linear arrangement.

How to Approach the Question

• First, identify the key information: there are 8 engineers, and each must discuss with every other one.
• Recognize that the order of discussion between two people doesn't create a new discussion (A talking to B is the same as B talking to A). This indicates a combination problem.
• Recall the formula for combinations of pairs, which is n × (n - 1) / 2, where 'n' is the number of people.
• Substitute n = 8 into the formula: 8 × (8 - 1) / 2.
• Calculate the result: 8 × 7 / 2 = 56 / 2 = 28.
• Compare the result with the given options to find the correct answer.

Concept Tested & Keywords

• Concept Tested: Combinations and Permutations
• Stem keywords: eight engineers, technical discussion, each one has to discuss with everyone else
• Lead-in keywords: How many

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Q5Oa7VPyMYsft0JLXOb8yo

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