Simple permutations question
December 17, 2024 2:30 PM Subscribe
I need an ELI5 on how to calculate permutations. My example below the fold.
A box can have:
1 color of 10 possible,
1 size of 5 possible,
1 integer of 20 possible.
How many combinations of boxes are possible? is it just 10 x 5 x 20?
A box can have:
1 color of 10 possible,
1 size of 5 possible,
1 integer of 20 possible.
How many combinations of boxes are possible? is it just 10 x 5 x 20?
As for how you can see this: Imagine you have a box that's 10 x 5 x 20. Any integer point in that box is valid. (This is perhaps easier to see in two dimensions where you can draw dots in a rectangle and label each choice.)
posted by hoyland at 9:10 PM on December 17 [1 favorite]
posted by hoyland at 9:10 PM on December 17 [1 favorite]
To make hoyland's visualization even more literal, think of one size of your literal box.
Now imagine 10 of that box, one of each color. A rainbow row of boxes.
Now 20 of those rows, each row's boxes labeled with one of the possible integers. But keep the rainbow in the same order in each row. So if you look at all the blue boxes, they will all be in a column, and each one will have a different integer -- each *column* might be labelled "1, 2, 3 , ... 20".
So you know how to find each color-integer combination, you have all of them and nothing duplicated, and there are 10 * 20 combinations.
For the sizes, each size makes that 10 * 20 grid, but you can stack them up at each spot -- a tower of five "purple, 11" boxes, say. Five layers, so we're up to 10 * 20 * 5. And the whole grid of stacks is like a 3 dimensional box itself, which is a real version of hoyland's box with integer point in it (integers would be, say, the center of each box).
posted by clew at 12:44 PM on December 18
Now imagine 10 of that box, one of each color. A rainbow row of boxes.
Now 20 of those rows, each row's boxes labeled with one of the possible integers. But keep the rainbow in the same order in each row. So if you look at all the blue boxes, they will all be in a column, and each one will have a different integer -- each *column* might be labelled "1, 2, 3 , ... 20".
So you know how to find each color-integer combination, you have all of them and nothing duplicated, and there are 10 * 20 combinations.
For the sizes, each size makes that 10 * 20 grid, but you can stack them up at each spot -- a tower of five "purple, 11" boxes, say. Five layers, so we're up to 10 * 20 * 5. And the whole grid of stacks is like a 3 dimensional box itself, which is a real version of hoyland's box with integer point in it (integers would be, say, the center of each box).
posted by clew at 12:44 PM on December 18
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(Things don't get complicated until you have to account for duplicates, which is not the case here.)
posted by demi-octopus at 2:38 PM on December 17 [7 favorites]