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 $\binom{24}{4}$.
Where am I going wrong?
Best Answer
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.