In how many different ways can you invest 20,000 onto five funds in increments of 1,000?
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In how many different ways can you invest 20,000 onto five funds in increments of 1,000?
(Question 4.24 from Timothy Falcon Crack)
The answer says it is $5^20$, but I thought of this as a "stars and bars" type of problem and said it was $binom244$.
Where am I going wrong?
combinatorics
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up vote
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favorite
In how many different ways can you invest 20,000 onto five funds in increments of 1,000?
(Question 4.24 from Timothy Falcon Crack)
The answer says it is $5^20$, but I thought of this as a "stars and bars" type of problem and said it was $binom244$.
Where am I going wrong?
combinatorics
1
Your first thousand can be invested in 1 of 5 funds. Your second thousand also have 1 of 5 possibilities....
â Jacky Chong
Aug 24 at 4:13
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
In how many different ways can you invest 20,000 onto five funds in increments of 1,000?
(Question 4.24 from Timothy Falcon Crack)
The answer says it is $5^20$, but I thought of this as a "stars and bars" type of problem and said it was $binom244$.
Where am I going wrong?
combinatorics
In how many different ways can you invest 20,000 onto five funds in increments of 1,000?
(Question 4.24 from Timothy Falcon Crack)
The answer says it is $5^20$, but I thought of this as a "stars and bars" type of problem and said it was $binom244$.
Where am I going wrong?
combinatorics
edited Aug 24 at 4:30
Jendrik Stelzner
7,57221037
7,57221037
asked Aug 24 at 4:09
jl_
82
82
1
Your first thousand can be invested in 1 of 5 funds. Your second thousand also have 1 of 5 possibilities....
â Jacky Chong
Aug 24 at 4:13
add a comment |Â
1
Your first thousand can be invested in 1 of 5 funds. Your second thousand also have 1 of 5 possibilities....
â Jacky Chong
Aug 24 at 4:13
1
1
Your first thousand can be invested in 1 of 5 funds. Your second thousand also have 1 of 5 possibilities....
â Jacky Chong
Aug 24 at 4:13
Your first thousand can be invested in 1 of 5 funds. Your second thousand also have 1 of 5 possibilities....
â Jacky Chong
Aug 24 at 4:13
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
3
down vote
accepted
You are thinking that each $1000$ is identical, so all that matters is how much money you put into each fund. If they are, your answer is correct. $5^20$ would be correct if the $1000$s were distinct. If you invested $1000$ per month for $20$ months it matters which $1000$ goes into which fund. They are different problems with different answers. Check the wording of the problem for whether the $1000$s are identical or distinct.
Thanks! That cleared it up. Not sure why the book didn't go into detail
â jl_
Aug 25 at 2:32
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
You are thinking that each $1000$ is identical, so all that matters is how much money you put into each fund. If they are, your answer is correct. $5^20$ would be correct if the $1000$s were distinct. If you invested $1000$ per month for $20$ months it matters which $1000$ goes into which fund. They are different problems with different answers. Check the wording of the problem for whether the $1000$s are identical or distinct.
Thanks! That cleared it up. Not sure why the book didn't go into detail
â jl_
Aug 25 at 2:32
add a comment |Â
up vote
3
down vote
accepted
You are thinking that each $1000$ is identical, so all that matters is how much money you put into each fund. If they are, your answer is correct. $5^20$ would be correct if the $1000$s were distinct. If you invested $1000$ per month for $20$ months it matters which $1000$ goes into which fund. They are different problems with different answers. Check the wording of the problem for whether the $1000$s are identical or distinct.
Thanks! That cleared it up. Not sure why the book didn't go into detail
â jl_
Aug 25 at 2:32
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
You are thinking that each $1000$ is identical, so all that matters is how much money you put into each fund. If they are, your answer is correct. $5^20$ would be correct if the $1000$s were distinct. If you invested $1000$ per month for $20$ months it matters which $1000$ goes into which fund. They are different problems with different answers. Check the wording of the problem for whether the $1000$s are identical or distinct.
You are thinking that each $1000$ is identical, so all that matters is how much money you put into each fund. If they are, your answer is correct. $5^20$ would be correct if the $1000$s were distinct. If you invested $1000$ per month for $20$ months it matters which $1000$ goes into which fund. They are different problems with different answers. Check the wording of the problem for whether the $1000$s are identical or distinct.
answered Aug 24 at 4:20
Ross Millikan
279k22188355
279k22188355
Thanks! That cleared it up. Not sure why the book didn't go into detail
â jl_
Aug 25 at 2:32
add a comment |Â
Thanks! That cleared it up. Not sure why the book didn't go into detail
â jl_
Aug 25 at 2:32
Thanks! That cleared it up. Not sure why the book didn't go into detail
â jl_
Aug 25 at 2:32
Thanks! That cleared it up. Not sure why the book didn't go into detail
â jl_
Aug 25 at 2:32
add a comment |Â
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1
Your first thousand can be invested in 1 of 5 funds. Your second thousand also have 1 of 5 possibilities....
â Jacky Chong
Aug 24 at 4:13