Permutations and Combinations help

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The discussion revolves around solving a problem involving permutations and combinations related to distributing articles between two people. The user outlines three cases of distribution but struggles to arrive at the correct answer of 14. It is clarified that the articles must be distinguishable for the calculations to be accurate. Each of the first two cases has four possibilities, while the third case has six, leading to the total of 14. Understanding the distinguishability of the articles is crucial for solving the problem correctly.
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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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