Indistinguishable objects

[schinb65]

An investor has 20000 to invest among 4 possible investments. Each investment must be a unit of 1000. If the total 20,000 must be invested, how many different investment strategies are possible? What if not all money need to be invested?
I should solve ${\binom{20000+4-1}{20000}}$? I think I need something with the 1000.

 

[Jameson]

Re: indestinguishable objects

Again, I must preface this with a disclaimer that I'm not confident about my solution.

1) I agree that it's \(\displaystyle \binom{3002}{3000}\). This isn't that big a number. What calculator are you using?

2) Since these must be in increments of 1000, I think it's really a problem of 20 objects in 4 spaces.

 

[schinb65]

Re: indestinguishable objects

Again, I must preface this with a disclaimer that I'm not confident about my solution.

1) I agree that it's \(\displaystyle \binom{3002}{3000}\). This isn't that big a number. What calculator are you using?

2) Since these must be in increments of 1000, I think it's really a problem of 20 objects in 4 spaces.

The calculator is a TI 84. I figured out the problem with the calculator. It computes the 3000! first then does the division. This number is too large but if you simplify the numbers it works. Thank you.

 

[schinb65]

Re: indestinguishable objects

Again, I must preface this with a disclaimer that I'm not confident about my solution.

1) I agree that it's \(\displaystyle \binom{3002}{3000}\). This isn't that big a number. What calculator are you using?

2) Since these must be in increments of 1000, I think it's really a problem of 20 objects in 4 spaces.

Thank you. The 1000 bring the values down to 20 objects gives me the correct answer. Thanks

 

[CellCoree]

I would approach this problem by first defining the variables and constraints. In this case, the investor has $20,000 to invest and there are 4 possible investments, each in units of $1000. Therefore, the total number of units available for investment is 20. We can also assume that the investor must invest all $20,000, as stated in the problem.

Using this information, we can solve for the number of different investment strategies using the formula for combinations, ${\binom{n}{k}}$, where n is the total number of units and k is the number of units per investment. In this case, n = 20 and k = 4, so we get ${\binom{20}{4}} = 4845$ possible investment strategies.

If the investor is not required to invest all $20,000, then the total number of units available for investment would be less than 20. In this case, we would use the formula for combinations with repetition, ${\binom{n+k-1}{n}}$, where n is the total number of units and k is the number of units per investment. For example, if the investor only needs to invest $15,000, then n = 15 and k = 4, giving us ${\binom{15+4-1}{15}} = {\binom{18}{15}} = 816$ possible investment strategies.

In summary, the number of different investment strategies possible depends on the total amount of money available for investment and the number of units per investment. By using the appropriate formula for combinations, we can accurately calculate the number of possible investment strategies.