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# help probability

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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
The text passage contains a probability question about distributing chocolates among friends and includes a detailed solution with combinatorial calculations.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
+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
user
The text passage contains a probability question about distributing chocolates among friends and includes a detailed solution with combinatorial calculations.

TYPE: SINGLE_QUESTION_WITH_ANSWER