MHB How Many Investment Strategies Are Possible with $20,000 and 4 Options?

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An investor can allocate $20,000 among four investment options, with each investment being a minimum of $1,000. The problem can be framed as distributing 20 indistinguishable objects (representing $1,000 increments) into 4 distinguishable spaces (the investment options). The correct formula to determine the number of investment strategies is \(\binom{3002}{3000}\), which simplifies the calculations. A TI-84 calculator can be used to compute this, but care must be taken to simplify the numbers to avoid overly large computations. The discussion emphasizes the importance of understanding the problem of indestinguishable objects in combinatorial mathematics.
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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.
 
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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 [math]\binom{3002}{3000}[/math]. 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.
 
Re: indestinguishable objects

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

1) I agree that it's [math]\binom{3002}{3000}[/math]. 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.
 
Re: indestinguishable objects

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

1) I agree that it's [math]\binom{3002}{3000}[/math]. 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
 
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