Number of ways to keep $20$ objects in $4$ boxes
-2
$begingroup$
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
edited Jan 4 at 4:20
max_zorn
3,36361329
asked Jan 4 at 3:41
Chand16Chand16
11
$endgroup$
|
show 2 more comments
-2
$begingroup$
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
edited Jan 4 at 4:20
max_zorn
3,36361329
asked Jan 4 at 3:41
Chand16Chand16
11
$endgroup$
2
$begingroup$
What have you tried so far?
$endgroup$
– Ben W
Jan 4 at 3:43
6
$begingroup$
This is the regrettably-named "stars and bars" problem. See here: math.stackexchange.com/questions/1441170/…
$endgroup$
– Ben W
Jan 4 at 3:56
$begingroup$
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.
$endgroup$
– dmtri
Jan 4 at 4:47
$begingroup$
@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.
$endgroup$
– JMoravitz
Jan 4 at 6:40
1
$begingroup$
@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.
$endgroup$
– JMoravitz
Jan 4 at 6:55
|
show 2 more comments
-2
-2
-2
$begingroup$
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
edited Jan 4 at 4:20
max_zorn
3,36361329
asked Jan 4 at 3:41
Chand16Chand16
11
$endgroup$
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
edited Jan 4 at 4:20
max_zorn
3,36361329
asked Jan 4 at 3:41
Chand16Chand16
11
edited Jan 4 at 4:20
max_zorn
3,36361329
asked Jan 4 at 3:41
Chand16Chand16
11
edited Jan 4 at 4:20
max_zorn
3,36361329
edited Jan 4 at 4:20
max_zorn
3,36361329
edited Jan 4 at 4:20
max_zorn
3,36361329
3,36361329
asked Jan 4 at 3:41
Chand16Chand16
11
asked Jan 4 at 3:41
Chand16Chand16
11
asked Jan 4 at 3:41
Chand16Chand16
11
11
2
$begingroup$
What have you tried so far?
$endgroup$
– Ben W
Jan 4 at 3:43
6
$begingroup$
This is the regrettably-named "stars and bars" problem. See here: math.stackexchange.com/questions/1441170/…
$endgroup$
– Ben W
Jan 4 at 3:56
$begingroup$
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.
$endgroup$
– dmtri
Jan 4 at 4:47
$begingroup$
@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.
$endgroup$
– JMoravitz
Jan 4 at 6:40
1
$begingroup$
@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.
$endgroup$
– JMoravitz
Jan 4 at 6:55
|
show 2 more comments
2
$begingroup$
What have you tried so far?
$endgroup$
– Ben W
Jan 4 at 3:43
6
$begingroup$
This is the regrettably-named "stars and bars" problem. See here: math.stackexchange.com/questions/1441170/…
$endgroup$
– Ben W
Jan 4 at 3:56
$begingroup$
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.
$endgroup$
– dmtri
Jan 4 at 4:47
$begingroup$
@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.
$endgroup$
– JMoravitz
Jan 4 at 6:40
1
$begingroup$
@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.
$endgroup$
– JMoravitz
Jan 4 at 6:55
2
2
$begingroup$
What have you tried so far?
$endgroup$
– Ben W
Jan 4 at 3:43
$begingroup$
What have you tried so far?
$endgroup$
– Ben W
Jan 4 at 3:43
6
6
$begingroup$
This is the regrettably-named "stars and bars" problem. See here: math.stackexchange.com/questions/1441170/…
$endgroup$
– Ben W
Jan 4 at 3:56
$begingroup$
This is the regrettably-named "stars and bars" problem. See here: math.stackexchange.com/questions/1441170/…
$endgroup$
– Ben W
Jan 4 at 3:56
$begingroup$
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.
$endgroup$
– dmtri
Jan 4 at 4:47
$begingroup$
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.
$endgroup$
– dmtri
Jan 4 at 4:47
$begingroup$
@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.
$endgroup$
– JMoravitz
Jan 4 at 6:40
$begingroup$
@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.
$endgroup$
– JMoravitz
Jan 4 at 6:40
1
1
$begingroup$
@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.
$endgroup$
– JMoravitz
Jan 4 at 6:55
$begingroup$
@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.
$endgroup$
– JMoravitz
Jan 4 at 6:55
|
show 2 more comments
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2
$begingroup$
What have you tried so far?
$endgroup$
– Ben W
Jan 4 at 3:43
6
$begingroup$
This is the regrettably-named "stars and bars" problem. See here: math.stackexchange.com/questions/1441170/…
$endgroup$
– Ben W
Jan 4 at 3:56
$begingroup$
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.
$endgroup$
– dmtri
Jan 4 at 4:47
$begingroup$
@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.
$endgroup$
– JMoravitz
Jan 4 at 6:40
1
$begingroup$
@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.
$endgroup$
– JMoravitz
Jan 4 at 6:55