Wikipedia:Category combinatorics

This page illustrates how categories of articles can be categorized in larger categories by means of combinatorics, binomial expansion, and Pascal's triangle.

Five factors

• Combination (1) of 5 factors

XXXXX: Category:Lists of American Jewish women scientists

• Combinations (5) of 4 factors

XXXX_: Category:Lists of American Jewish women,

XXX_X: Category:Lists of American Jewish scientists,

XX_XX: Category:Lists of American women scientists,

X_XXX: Category:Lists of Jewish women scientists,

_XXXX: Category:American Jewish women scientists

• Combinations (10) of 3 factors

XXX__: Category:Lists of American Jews,

XX_X_: Category:Lists of American women,

X_XX_: Category:Lists of Jewish women,

_XXX_: Category:American Jewish women,

XX__X: Category:Lists of American scientists,

X_X_X: Category:Lists of Jewish scientists,

_XX_X: Category:American Jewish scientists,

X__XX: Category:Lists of women scientists,

_X_XX: Category:American women scientists,

__XXX: Category:Jewish women scientists

• Combinations (10) of 2 factors

XX___: Category:Lists of Americans,

X_X__: Category:Lists of Jews,

X__X_: Category:Lists of women,

X___X: Category:Lists of scientists,

_XX__: Category:American Jews,

__X_X: Category:American women,

_X__X: Category:American scientists,

__XX_: Category:Jewish women,

__X_X: Category:Jewish scientists,

___XX: Category:Women scientists

• Combinations (5) of 1 factor

X____: Category:Lists,

_X___: Category:Americans,

__X__: Category:Jews,

___X_: Category:Women,

____X: Category:Scientists

• Combination (1) of 0 factor

_____: Category:Contents

• 1 + 5 + 10 + 10 + 5 + 1 = 32 = 2 × 2 × 2 × 2 × 2