How many ways are there? [closed]
How many ways are there to put 14 identical objects in 3 distinct boxes with at least 8 objects in one box?
What is the thinking procedure of the similar question type?
combinatorics combinations
edited Dec 11 '18 at 9:43
N. F. Taussig
43.6k93355
asked Dec 11 '18 at 7:03
CCola
275
closed as off-topic by choco_addicted, Henrik, Cesareo, GNUSupporter 8964民主女神 地下教會, José Carlos Santos Dec 11 '18 at 11:52
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – choco_addicted, Henrik, Cesareo, GNUSupporter 8964民主女神 地下教會, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
How many ways are there to put 14 identical objects in 3 distinct boxes with at least 8 objects in one box?
What is the thinking procedure of the similar question type?
combinatorics combinations
edited Dec 11 '18 at 9:43
N. F. Taussig
43.6k93355
asked Dec 11 '18 at 7:03
CCola
275
closed as off-topic by choco_addicted, Henrik, Cesareo, GNUSupporter 8964民主女神 地下教會, José Carlos Santos Dec 11 '18 at 11:52
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – choco_addicted, Henrik, Cesareo, GNUSupporter 8964民主女神 地下教會, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
2
If you don't regard the condition with 8 objects in the beginning, the problem is similar to finding the number of integer solutions to $$ x_1 + x_2 + x_3 = 14-8 $$
– Matti P.
Dec 11 '18 at 7:04
2
I think you have to multiply above result by 3 ? @MattiP.
– rsadhvika
Dec 11 '18 at 7:14
2
@rsadhvika I agree. Multiplying by 3 takes into account the 8 objects in the beginning.
– Matti P.
Dec 11 '18 at 7:15
I suggest looking up "generating functions" as a way to solve these integer problems.
– Aditya Dua
Dec 11 '18 at 7:17
add a comment |
How many ways are there to put 14 identical objects in 3 distinct boxes with at least 8 objects in one box?
What is the thinking procedure of the similar question type?
combinatorics combinations
edited Dec 11 '18 at 9:43
N. F. Taussig
43.6k93355
asked Dec 11 '18 at 7:03
CCola
275
How many ways are there to put 14 identical objects in 3 distinct boxes with at least 8 objects in one box?
What is the thinking procedure of the similar question type?
combinatorics combinations
combinatorics combinations
edited Dec 11 '18 at 9:43
N. F. Taussig
43.6k93355
asked Dec 11 '18 at 7:03
CCola
275
edited Dec 11 '18 at 9:43
N. F. Taussig
43.6k93355
asked Dec 11 '18 at 7:03
CCola
275
edited Dec 11 '18 at 9:43
N. F. Taussig
43.6k93355
edited Dec 11 '18 at 9:43
N. F. Taussig
43.6k93355
edited Dec 11 '18 at 9:43
N. F. Taussig
43.6k93355
43.6k93355
asked Dec 11 '18 at 7:03
CCola
275
asked Dec 11 '18 at 7:03
CCola
275
asked Dec 11 '18 at 7:03
CCola
275
275
closed as off-topic by choco_addicted, Henrik, Cesareo, GNUSupporter 8964民主女神 地下教會, José Carlos Santos Dec 11 '18 at 11:52
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – choco_addicted, Henrik, Cesareo, GNUSupporter 8964民主女神 地下教會, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by choco_addicted, Henrik, Cesareo, GNUSupporter 8964民主女神 地下教會, José Carlos Santos Dec 11 '18 at 11:52
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – choco_addicted, Henrik, Cesareo, GNUSupporter 8964民主女神 地下教會, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
2
If you don't regard the condition with 8 objects in the beginning, the problem is similar to finding the number of integer solutions to $$ x_1 + x_2 + x_3 = 14-8 $$
– Matti P.
Dec 11 '18 at 7:04
2
I think you have to multiply above result by 3 ? @MattiP.
– rsadhvika
Dec 11 '18 at 7:14
2
@rsadhvika I agree. Multiplying by 3 takes into account the 8 objects in the beginning.
– Matti P.
Dec 11 '18 at 7:15
I suggest looking up "generating functions" as a way to solve these integer problems.
– Aditya Dua
Dec 11 '18 at 7:17
add a comment |
2
If you don't regard the condition with 8 objects in the beginning, the problem is similar to finding the number of integer solutions to $$ x_1 + x_2 + x_3 = 14-8 $$
– Matti P.
Dec 11 '18 at 7:04
2
I think you have to multiply above result by 3 ? @MattiP.
– rsadhvika
Dec 11 '18 at 7:14
2
@rsadhvika I agree. Multiplying by 3 takes into account the 8 objects in the beginning.
– Matti P.
Dec 11 '18 at 7:15
I suggest looking up "generating functions" as a way to solve these integer problems.
– Aditya Dua
Dec 11 '18 at 7:17
2
2
If you don't regard the condition with 8 objects in the beginning, the problem is similar to finding the number of integer solutions to $$ x_1 + x_2 + x_3 = 14-8 $$
– Matti P.
Dec 11 '18 at 7:04
If you don't regard the condition with 8 objects in the beginning, the problem is similar to finding the number of integer solutions to $$ x_1 + x_2 + x_3 = 14-8 $$
– Matti P.
Dec 11 '18 at 7:04
2
2
I think you have to multiply above result by 3 ? @MattiP.
– rsadhvika
Dec 11 '18 at 7:14
I think you have to multiply above result by 3 ? @MattiP.
– rsadhvika
Dec 11 '18 at 7:14
2
2
@rsadhvika I agree. Multiplying by 3 takes into account the 8 objects in the beginning.
– Matti P.
Dec 11 '18 at 7:15
@rsadhvika I agree. Multiplying by 3 takes into account the 8 objects in the beginning.
– Matti P.
Dec 11 '18 at 7:15
I suggest looking up "generating functions" as a way to solve these integer problems.
– Aditya Dua
Dec 11 '18 at 7:17
I suggest looking up "generating functions" as a way to solve these integer problems.
– Aditya Dua
Dec 11 '18 at 7:17
add a comment |
1 Answer
1
active
oldest
votes
You have to find a unique way to describe a possible placement of the objects, that makes counting easy. Here is a solution.
- Choose the box that has at least $8$ objects: $3$ choices.
- For each of the preceding choices, let $k$ be the number of objects in this box ($8le kle 14$).
- For each $k$, choose the number of objects in the leftmost remaining box ($0$ to $14-k$): $15-k$ choices.
- The last box gets the remaining.
This uniquely describes the three boxes.
How many choices now?
$$3sum_{k=8}^{14} (15-k)$$
answered Dec 11 '18 at 7:19
Jean-Claude Arbaut
14.7k63464
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
You have to find a unique way to describe a possible placement of the objects, that makes counting easy. Here is a solution.
- Choose the box that has at least $8$ objects: $3$ choices.
- For each of the preceding choices, let $k$ be the number of objects in this box ($8le kle 14$).
- For each $k$, choose the number of objects in the leftmost remaining box ($0$ to $14-k$): $15-k$ choices.
- The last box gets the remaining.
This uniquely describes the three boxes.
How many choices now?
$$3sum_{k=8}^{14} (15-k)$$
answered Dec 11 '18 at 7:19
Jean-Claude Arbaut
14.7k63464
add a comment |
You have to find a unique way to describe a possible placement of the objects, that makes counting easy. Here is a solution.
- Choose the box that has at least $8$ objects: $3$ choices.
- For each of the preceding choices, let $k$ be the number of objects in this box ($8le kle 14$).
- For each $k$, choose the number of objects in the leftmost remaining box ($0$ to $14-k$): $15-k$ choices.
- The last box gets the remaining.
This uniquely describes the three boxes.
How many choices now?
$$3sum_{k=8}^{14} (15-k)$$
answered Dec 11 '18 at 7:19
Jean-Claude Arbaut
14.7k63464
add a comment |
You have to find a unique way to describe a possible placement of the objects, that makes counting easy. Here is a solution.
- Choose the box that has at least $8$ objects: $3$ choices.
- For each of the preceding choices, let $k$ be the number of objects in this box ($8le kle 14$).
- For each $k$, choose the number of objects in the leftmost remaining box ($0$ to $14-k$): $15-k$ choices.
- The last box gets the remaining.
This uniquely describes the three boxes.
How many choices now?
$$3sum_{k=8}^{14} (15-k)$$
answered Dec 11 '18 at 7:19
Jean-Claude Arbaut
14.7k63464
You have to find a unique way to describe a possible placement of the objects, that makes counting easy. Here is a solution.
- Choose the box that has at least $8$ objects: $3$ choices.
- For each of the preceding choices, let $k$ be the number of objects in this box ($8le kle 14$).
- For each $k$, choose the number of objects in the leftmost remaining box ($0$ to $14-k$): $15-k$ choices.
- The last box gets the remaining.
This uniquely describes the three boxes.
How many choices now?
$$3sum_{k=8}^{14} (15-k)$$
answered Dec 11 '18 at 7:19
Jean-Claude Arbaut
14.7k63464
answered Dec 11 '18 at 7:19
Jean-Claude Arbaut
14.7k63464
answered Dec 11 '18 at 7:19
Jean-Claude Arbaut
14.7k63464
answered Dec 11 '18 at 7:19
Jean-Claude Arbaut
14.7k63464
14.7k63464
add a comment |
add a comment |
2
If you don't regard the condition with 8 objects in the beginning, the problem is similar to finding the number of integer solutions to $$ x_1 + x_2 + x_3 = 14-8 $$
– Matti P.
Dec 11 '18 at 7:04
2
I think you have to multiply above result by 3 ? @MattiP.
– rsadhvika
Dec 11 '18 at 7:14
2
@rsadhvika I agree. Multiplying by 3 takes into account the 8 objects in the beginning.
– Matti P.
Dec 11 '18 at 7:15
I suggest looking up "generating functions" as a way to solve these integer problems.
– Aditya Dua
Dec 11 '18 at 7:17