I'm trying to figure out the possible combinations of a group of objects each priced differently.

Question

There are 16 objects priced as follows:

$9,600

$9,400

$9,200

$8,800

$8,600

$8,400

$7,800

$7,200

$7,000

$6,600

$6,200

$5,800

$5,400

$5,000

$4,800

and finally $4,600

I have a budget of $50,000. How many combinations of 6 items could I buy without going over the budget? And what are those combinations?

Answer 1

This is NOT a plain vanilla combinations problem - https://www.mathcelebrity.com/permutation.php?num=16&den=6&pl=Combinations

The prices and budget constraint demand one form or another of brute force to solve. You cannot directly calculate your answer. There exist 8,008 combinations of 6 from 16, but not all of them conform with being < $50,000. Which 6s work is dependent on the 16 specific values.

STEP 1 - identify the 8,008 sets of 6

This process can probably get your answer in a spreadsheet - https://exceloffthegrid.com/list-of-all-possible-combinations-using-power-query/

Here is how to get the list with Python - https://docs.python.org/3/library/itertools.html#itertools.combinations

STEP 2 - Calculate each set's value

Once you have the list, you can calculate the value of each combination and count how many are < $50,000. If you got the list, identifying the value of each item will be a breeze.