text: +0
  
  # help probability
  
  0
  152
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  Miyu is giving out 9 identical chocolates to her 7 friends, including Dhruv.  All possible distributions are equally likely.  What is the probability that Dhruv gets exactly 2 chocolates?
  
  Dec 14, 2022
  
  #1
  +2667
  0
  
  9 chocolates, 7 friends = 9 stars, 6 bars. So, there are $${15 \choose 6} = 5005$$ combinations.
  
  If Dhruv gets 2, there are 5 chocolates for 6 people, which means there are 7 stars and 5 bars, making for $${12 \choose 5} = 792$$ cases
  
  So, the probabilty is $${792 \over 5005} = \color{brown}\boxed{72 \over 455}$$
  
  Dec 14, 2022
explanation: The document contains a probability question and its corresponding answer. The question is about calculating the probability that Dhruv gets exactly 2 chocolates when 9 identical chocolates are distributed among 7 friends. The answer uses combinatorial methods to determine the probability.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: +0
  
  # help probability
  
  0
  152
  1
  
  Miyu is giving out 9 identical chocolates to her 7 friends, including Dhruv.  All possible distributions are equally likely.  What is the probability that Dhruv gets exactly 2 chocolates?
  
  Dec 14, 2022
  
  #1
  +2667
  0
  
  9 chocolates, 7 friends = 9 stars, 6 bars. So, there are $${15 \choose 6} = 5005$$ combinations.
  
  If Dhruv gets 2, there are 5 chocolates for 6 people, which means there are 7 stars and 5 bars, making for $${12 \choose 5} = 792$$ cases
  
  So, the probabilty is $${792 \over 5005} = \color{brown}\boxed{72 \over 455}$$
  
  Dec 14, 2022
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a probability question and its corresponding answer. The question is about calculating the probability that Dhruv gets exactly 2 chocolates when 9 identical chocolates are distributed among 7 friends. The answer uses combinatorial methods to determine the probability.
  
  Label: question-and-answer