Number of ways to keep $20$ objects in $4$ boxes
Ben has $20$ identical marbles. In how many different ways he can put all $20$ marbles in $4$
different boxes? (He may choose to keep one or more boxes empty)
combinatorics
New contributor
|
show 2 more comments
Ben has $20$ identical marbles. In how many different ways he can put all $20$ marbles in $4$
different boxes? (He may choose to keep one or more boxes empty)
combinatorics
New contributor
2
What have you tried so far?
– Ben W
Jan 4 at 3:43
6
This is the regrettably-named "stars and bars" problem. See here: math.stackexchange.com/questions/1441170/…
– Ben W
Jan 4 at 3:56
Make a row of 20 marbles, then put 3 vertical bars in between. How many ways are there to do this? Take also the case where some boxes are empty.
– dmtri
Jan 4 at 4:47
@BenW Why do you say it is "regrettably-named"? One of the common explanations for the solution is by making a bijection to the ways in which you may lay out an appropriate number of stars and an appropriate number of bars in a line... the answer of how many ways in which that can be accomplished usually being much more intuitive for many students. In the same way as any 50-50 scenarios can be called "effectively a coin flip" even if the specific scenario itself has nothing to do with coins, so too can this problem be referred to by stars-and-bars even if the original phrasing has neither.
– JMoravitz
Jan 4 at 6:40
1
@BenW feeling that the name for the combinatorial problem being "stars-and-bars" is a painful reminder of a darker part of American history due to the similarity in name to one of the earlier versions of the flag of the confederacy (and not even the flag most commonly associated with) feels on the same level to me as choosing not to trust someone whose name is Bill because of the actions of an actor by that name. I think the benefit of having an aptly descriptive name outweighs any potential tangential reminder to history.
– JMoravitz
Jan 4 at 6:55
|
show 2 more comments
Ben has $20$ identical marbles. In how many different ways he can put all $20$ marbles in $4$
different boxes? (He may choose to keep one or more boxes empty)
combinatorics
New contributor
Ben has $20$ identical marbles. In how many different ways he can put all $20$ marbles in $4$
different boxes? (He may choose to keep one or more boxes empty)
combinatorics
combinatorics
New contributor
New contributor
edited Jan 4 at 4:20
max_zorn
3,29361328
3,29361328
New contributor
asked Jan 4 at 3:41
Chand16Chand16
11
11
New contributor
New contributor
2
What have you tried so far?
– Ben W
Jan 4 at 3:43
6
This is the regrettably-named "stars and bars" problem. See here: math.stackexchange.com/questions/1441170/…
– Ben W
Jan 4 at 3:56
Make a row of 20 marbles, then put 3 vertical bars in between. How many ways are there to do this? Take also the case where some boxes are empty.
– dmtri
Jan 4 at 4:47
@BenW Why do you say it is "regrettably-named"? One of the common explanations for the solution is by making a bijection to the ways in which you may lay out an appropriate number of stars and an appropriate number of bars in a line... the answer of how many ways in which that can be accomplished usually being much more intuitive for many students. In the same way as any 50-50 scenarios can be called "effectively a coin flip" even if the specific scenario itself has nothing to do with coins, so too can this problem be referred to by stars-and-bars even if the original phrasing has neither.
– JMoravitz
Jan 4 at 6:40
1
@BenW feeling that the name for the combinatorial problem being "stars-and-bars" is a painful reminder of a darker part of American history due to the similarity in name to one of the earlier versions of the flag of the confederacy (and not even the flag most commonly associated with) feels on the same level to me as choosing not to trust someone whose name is Bill because of the actions of an actor by that name. I think the benefit of having an aptly descriptive name outweighs any potential tangential reminder to history.
– JMoravitz
Jan 4 at 6:55
|
show 2 more comments
2
What have you tried so far?
– Ben W
Jan 4 at 3:43
6
This is the regrettably-named "stars and bars" problem. See here: math.stackexchange.com/questions/1441170/…
– Ben W
Jan 4 at 3:56
Make a row of 20 marbles, then put 3 vertical bars in between. How many ways are there to do this? Take also the case where some boxes are empty.
– dmtri
Jan 4 at 4:47
@BenW Why do you say it is "regrettably-named"? One of the common explanations for the solution is by making a bijection to the ways in which you may lay out an appropriate number of stars and an appropriate number of bars in a line... the answer of how many ways in which that can be accomplished usually being much more intuitive for many students. In the same way as any 50-50 scenarios can be called "effectively a coin flip" even if the specific scenario itself has nothing to do with coins, so too can this problem be referred to by stars-and-bars even if the original phrasing has neither.
– JMoravitz
Jan 4 at 6:40
1
@BenW feeling that the name for the combinatorial problem being "stars-and-bars" is a painful reminder of a darker part of American history due to the similarity in name to one of the earlier versions of the flag of the confederacy (and not even the flag most commonly associated with) feels on the same level to me as choosing not to trust someone whose name is Bill because of the actions of an actor by that name. I think the benefit of having an aptly descriptive name outweighs any potential tangential reminder to history.
– JMoravitz
Jan 4 at 6:55
2
2
What have you tried so far?
– Ben W
Jan 4 at 3:43
What have you tried so far?
– Ben W
Jan 4 at 3:43
6
6
This is the regrettably-named "stars and bars" problem. See here: math.stackexchange.com/questions/1441170/…
– Ben W
Jan 4 at 3:56
This is the regrettably-named "stars and bars" problem. See here: math.stackexchange.com/questions/1441170/…
– Ben W
Jan 4 at 3:56
Make a row of 20 marbles, then put 3 vertical bars in between. How many ways are there to do this? Take also the case where some boxes are empty.
– dmtri
Jan 4 at 4:47
Make a row of 20 marbles, then put 3 vertical bars in between. How many ways are there to do this? Take also the case where some boxes are empty.
– dmtri
Jan 4 at 4:47
@BenW Why do you say it is "regrettably-named"? One of the common explanations for the solution is by making a bijection to the ways in which you may lay out an appropriate number of stars and an appropriate number of bars in a line... the answer of how many ways in which that can be accomplished usually being much more intuitive for many students. In the same way as any 50-50 scenarios can be called "effectively a coin flip" even if the specific scenario itself has nothing to do with coins, so too can this problem be referred to by stars-and-bars even if the original phrasing has neither.
– JMoravitz
Jan 4 at 6:40
@BenW Why do you say it is "regrettably-named"? One of the common explanations for the solution is by making a bijection to the ways in which you may lay out an appropriate number of stars and an appropriate number of bars in a line... the answer of how many ways in which that can be accomplished usually being much more intuitive for many students. In the same way as any 50-50 scenarios can be called "effectively a coin flip" even if the specific scenario itself has nothing to do with coins, so too can this problem be referred to by stars-and-bars even if the original phrasing has neither.
– JMoravitz
Jan 4 at 6:40
1
1
@BenW feeling that the name for the combinatorial problem being "stars-and-bars" is a painful reminder of a darker part of American history due to the similarity in name to one of the earlier versions of the flag of the confederacy (and not even the flag most commonly associated with) feels on the same level to me as choosing not to trust someone whose name is Bill because of the actions of an actor by that name. I think the benefit of having an aptly descriptive name outweighs any potential tangential reminder to history.
– JMoravitz
Jan 4 at 6:55
@BenW feeling that the name for the combinatorial problem being "stars-and-bars" is a painful reminder of a darker part of American history due to the similarity in name to one of the earlier versions of the flag of the confederacy (and not even the flag most commonly associated with) feels on the same level to me as choosing not to trust someone whose name is Bill because of the actions of an actor by that name. I think the benefit of having an aptly descriptive name outweighs any potential tangential reminder to history.
– JMoravitz
Jan 4 at 6:55
|
show 2 more comments
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Chand16 is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3061297%2fnumber-of-ways-to-keep-20-objects-in-4-boxes%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Chand16 is a new contributor. Be nice, and check out our Code of Conduct.
Chand16 is a new contributor. Be nice, and check out our Code of Conduct.
Chand16 is a new contributor. Be nice, and check out our Code of Conduct.
Chand16 is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3061297%2fnumber-of-ways-to-keep-20-objects-in-4-boxes%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
2
What have you tried so far?
– Ben W
Jan 4 at 3:43
6
This is the regrettably-named "stars and bars" problem. See here: math.stackexchange.com/questions/1441170/…
– Ben W
Jan 4 at 3:56
Make a row of 20 marbles, then put 3 vertical bars in between. How many ways are there to do this? Take also the case where some boxes are empty.
– dmtri
Jan 4 at 4:47
@BenW Why do you say it is "regrettably-named"? One of the common explanations for the solution is by making a bijection to the ways in which you may lay out an appropriate number of stars and an appropriate number of bars in a line... the answer of how many ways in which that can be accomplished usually being much more intuitive for many students. In the same way as any 50-50 scenarios can be called "effectively a coin flip" even if the specific scenario itself has nothing to do with coins, so too can this problem be referred to by stars-and-bars even if the original phrasing has neither.
– JMoravitz
Jan 4 at 6:40
1
@BenW feeling that the name for the combinatorial problem being "stars-and-bars" is a painful reminder of a darker part of American history due to the similarity in name to one of the earlier versions of the flag of the confederacy (and not even the flag most commonly associated with) feels on the same level to me as choosing not to trust someone whose name is Bill because of the actions of an actor by that name. I think the benefit of having an aptly descriptive name outweighs any potential tangential reminder to history.
– JMoravitz
Jan 4 at 6:55