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Four boxes with ball capacity of 3 , 5 , 7 and 8 are given . In how many ways can 19 same balls be put together in these boxes .

Darkside  Aug 18, 2018
 #1
avatar
+1

Here is my attempt at distributing the 19 balls. Please be warned that this may be wrong! Take it at your own peril !!!!:

 

1-    8 + 7 + 3 + 1 = 19
2-   8 + 7 + 2 + 2 = 19
3-   8 + 6 + 4 + 1 = 19
4-   8 + 6 + 3 + 2 = 19
5-    8 + 5 + 5 + 1 = 19
6-   8 + 5 + 4 + 2 = 19
7-   8 + 5 + 3 + 3 = 19
8-   8 + 4 + 4 + 3 = 19
9-    7 + 7 + 4 + 1 = 19
10-  7 + 7 + 3 + 2 = 19
11-  7 + 6 + 5 + 1 = 19
12-  7 + 6 + 4 + 2 = 19
13-  7 + 6 + 3 + 3 = 19
14-  7 + 5 + 5 + 2 = 19
15-  7 + 5 + 4 + 3 = 19
16-  6 + 6 + 5 + 2 = 19
17-  6 + 6 + 4 + 3 = 19
18-  6 + 5 + 5 + 3 = 19

The capacity of the boxes is counted from left to right as: 8, 7, 5, 3

Guest Aug 18, 2018
 #2
avatar
+1

1 - above can have one additional arrangement: 8 + 7 + 1 + 3........19

4- above .............................................................: 8 + 6 + 2 + 3........20

10 - above............................................................: 7 + 7 + 2 + 3.........21

11- above..............................................................: 6+ 7 + 5 + 1.........22

12 - above.............................................................: 6 + 7 + 4 + 2........23

13-above................................................................: 6 + 7 + 3 + 3.......24

14- above................................................................: 5 + 7 + 5 + 2.......25

15- above.................................................................:5 + 7 + 4 + 3.......26

16-above..................................................................: 6 + 7 + 5 + 1...... 27

                                                                                    6 + 7 + 4 + 2.......28

                                                                                    6 + 7 + 3 + 3.......29

18-above...................................................................: 5 + 6 + 5 + 3.......30

So, it looks that in addition to the 18 listed above, you can have another 12 arrangements for a grand total =30

Guest Aug 20, 2018
 #3
avatar+93342 
+1

A question to the 2 answering guests.

Why can't one of the boxes be empty?     

0,4,7,8

0,5,6,8

0,5,7,7

Melody  Aug 21, 2018
 #4
avatar+20009 
+1

Four boxes with ball capacity of 3 , 5 , 7 and 8 are given .

In how many ways can 19 same balls be put together in these boxes .

 

\(\begin{array}{|r|cccc|} \hline &\text{Box with} &\text{Box with}& \text{Box with}& \text{Box with} \\ &\text{capacity of 8} & \text{capacity of 7}& \text{capacity of 5} & \text{capacity of 3} \\ \hline 1. & 4 & 7 & 5& 3 \\ 2. & 5 & 6 & 5& 3 \\ 3. & 5 & 7 & 4& 3 \\ 4. & 5 & 7 & 5& 2 \\ 5. & 6 & 5 & 5& 3 \\ 6. & 6 & 6 & 4& 3 \\ 7. & 6 & 6 & 5& 2 \\ 8. & 6 & 7 & 3& 3 \\ 9. & 6 & 7 & 4& 2 \\ 10. & 6& 7 & 5& 1 \\ 11. & 7& 4 & 5& 3 \\ 12. & 7& 5 & 4& 3 \\ 13. & 7& 5 & 5& 2 \\ 14. & 7& 6 & 3& 3 \\ 15. & 7& 6 & 4& 2 \\ 16. & 7& 6 & 5& 1 \\ 17. & 7& 7 & 2& 3 \\ 18. & 7& 7 & 3& 2 \\ 19. & 7& 7 & 4& 1 \\ 20. & 7& 7 & 5& 0 \\ 21. & 8& 3 & 5& 3 \\ 22. & 8& 4 & 4& 3 \\ 23. & 8& 4 & 5& 2 \\ 24. & 8& 5 & 3& 3 \\ 25. & 8& 5 & 4& 2 \\ 26. & 8& 5 & 5& 1 \\ 27. & 8& 6 & 2& 3 \\ 28. & 8& 6 & 3& 2 \\ 29. & 8& 6 & 4& 1 \\ 30. & 8& 6 & 5& 0 \\ 31. & 8& 7 & 1& 3 \\ 32. & 8& 7 & 2& 2 \\ 33. & 8& 7 & 3& 1 \\ 34. & 8& 7 & 4& 0 \\ \hline \end{array} \)

 

 

laugh

heureka  Aug 21, 2018

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