Permutations and Combinations help

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SUMMARY

The discussion focuses on solving a combinatorial problem involving permutations and combinations, specifically regarding distributing 4 distinguishable articles between 2 people. The user initially considers three cases: one where the first person receives 1 article and the second receives 3, another where the first receives 3 and the second receives 1, and a third where both receive 2 articles. The correct total number of distributions is confirmed to be 14, derived from the fact that cases 1 and 2 each have 4 possibilities, while case 3 has 6 possibilities, leading to the final calculation of 4 + 4 + 6 = 14.

PREREQUISITES
  • Understanding of permutations and combinations
  • Knowledge of distinguishable versus indistinguishable objects
  • Basic principles of dependent events in probability
  • Familiarity with combinatorial problem-solving techniques
NEXT STEPS
  • Study the principles of permutations and combinations in detail
  • Learn about distinguishable and indistinguishable objects in combinatorial contexts
  • Explore dependent and independent events in probability theory
  • Practice solving similar combinatorial problems to reinforce understanding
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Students, educators, and professionals in mathematics, statistics, and computer science who are looking to enhance their understanding of combinatorial concepts and problem-solving strategies.

Ronaldo95163
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Having problems with question 9 and what I came up was Case 1:
1st person gets 1 And
2nd person gets 3

OR

Case 2:
1st person gets 3 And
2nd person gets 1

OR

Case 3
They both get 2

And seeing that they are both dependent events so that once a person receives an article it affects the amount the next person gets. I used permutations for each of the two scenarios for each case, multiplied them and added them all together but I don't get the correct answer which is 14. What am I doing wrong?
 

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Ronaldo95163 said:
Having problems with question 9 and what I came up wasCase 1:
1st person gets 1 And
2nd person gets 3

OR

Case 2:
1st person gets 3 And
2nd person gets 1

OR

Case 3
They both get 2

And seeing that they are both dependent events so that once a person receives an article it affects the amount the next person gets. I used permutations for each of the two scenarios for each case, multiplied them and added them all together but I don't get the correct answer which is 14. What am I doing wrong?
Are the articles supposed to be distinguishable? Do you reckon it matters?
 
As long as the 4 articles are distinguishable, 14 is correct. Cases 1 and 2 have 4 possibilities each, while case 3 has 6.
 

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