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combinations vs permutations

can you add a line separating each row so that the solution can just be combinations vs permutations without having to specify that it is about rows

or the solution can be "rows in each box show all possible combinations of sorting dots into bins vs rows in each box show all possible permutations of sorting dots into bins"

In the box on the left with 6 bins, there are 5 empty bins and 1 bin with 1 dot. The position of the bin with 1 dot does not create a unique combination of bins because there are still 5 empty and 1 with 1.

In the box on the right with a 3 by 3 grid of bins, the position of the bin with the dot creates a unique permutation. 1-0-0, 0-1-0, 0-0-1 are considered unique on the right, but the same on the left.

A null box would fit on either side, as would any singular box with any amount of dots. (does that make this problem invalid?)

order of bins does not matter on the left, order of bins matters on the right

rows are all possible combinations, order of bins not considered, of x dots into r bins vs notso

The order of the bins in each row does not matter in this problem. For example, if we have 4 bins with 0, 1, 1, and 0 dots in each, this is considered the same as having 4 bins in the order 0, 0, 1, 1, or 1, 0, 0, 1, and so on. Boxes on right side are invalid either because they do not have the same number of dots in each row or because they have rows of bins that are considered to be the same combination of dots.

my previous BP of permutations

all possible permutations of x number of dots into r number of bins in each row vs notso

I included combinatorics words in the concepts. I will make more BPs with these concepts tagged.

planar (all lines connecting dots can be uncrossed) vs non-planar (not all lines can be uncrossed)

ignore gray lines

not important that each square contains 6 dots

I included graph theory words in the concepts appearing in this BP. I will probably make more graph theory BPs and use these same concepts.

Richard J. Trudeau, Introduction to Graph Theory, 1975.

ignore gray line

disphenoid aka tetrahedron that is isosceles or scalene

Aaron Fairbanks had another valid solution for this one about how the angles in the triangles are arranged: "Some smaller angles connected to larger angles vs. not so"

folds into disphenoid vs cannot fold into disphenoid

ignore gray line

disphenoid aka isosceles tetrahedron

Aaron Fairbanks had another valid solution for this one about how the angles in the triangles are arranged: "Some smaller angles connected to larger angles vs. not so"

Molly C Klenzak

Bongard Problems with world one small equilateral triangle outline and one small circle outline vs other Bongard Problems.

These outlines not allowed to overlap.

Aaron David Fairbanks