harry potter - How many possible types of wands can Ollivander make?

How many possible types of wands can Ollivander make, if the variables are only core material, wood material, and length in inches?

_{This is a small subquestion related to this, and intended to establish a definite cap on how many maximum possible wands would a wizard be able to choose from (assuming, for any wizard, SOME wand will always choose him, with the choice determined by core material, wood material, and length)}

Please note that the combinations are finite, based on Pottermore, since Ollivander does not use random materials.

Answer

Fortunately for the sake of a reasonable answer, Ollivanders limits himself greatly as to which wands he will actually make. From Pottermore, articles on Wandlore:

Every single wand is unique and will depend for its character on the particular tree and magical creature from which it derives its materials. Moreover, each wand, from the moment it finds its ideal owner, will begin to learn from and teach its human partner. Therefore, the following must be seen as general notes on each of the wood types I like to work with best, and ought not to be taken to describe any individual wand.

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Only a minority of trees can produce wand quality wood (just as a minority of humans can produce magic).

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Most wands will be in the range of between nine and fourteen inches. While I have sold extremely short wands (eight inches and under) and very long wands (over fifteen inches), these are exceptionally rare.

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Wand flexibility or rigidity denotes the degree of adaptability and willingness to change possessed by the wand-and-owner pair - although, again, this factor ought not to be considered separately from the wand wood, core and length, nor of the owner’s life experience and style of magic, all of which will combine to make the wand in question unique.

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Early in my career, as I watched my wandmaker father wrestling with substandard wand core materials such as kelpie hair, I conceived the ambition to discover the finest cores and to work only with those when my time came to take over the family business. This I have done. After much experimentation and research, I concluded that only three substances produce wands of the quality to which I am happy to give the illustrious name of Ollivander: unicorn hair, dragon heartstring and phoenix feather.

Now, that limits it greatly. Ollivander sells wands made from thirty-eight different woods, listed here: Acacia, Alder, Applewood, Ash, Aspen, Beech, Blackthorn, Black Walnut, Cedar, Cherry, Chestnut, Cypress, Dogwood, Ebony, Elder, Elm, English Oak, Fir, Hawthorn, Hazel, Holly, Hornbeam, Larch, Laurel, Maple, Pear, Pine, Poplar, Red Oak, Redwood, Rowan, Silver lime, Spruce, Sycamore, Vine, Walnut, Willow, Yew.

Ollivander sells wands of three cores: phoenix feather, dragon heartstring, and unicorn tail hair.

Ollivander sells wands that are categorized as having one of eight distinct flexibilities: Unyielding, Hard, Rigid, Brittle, Reasonably Supple, Slightly Springy, Surprisingly Swishy, Quite Flexible.

The final variable is length. According to Pottermore, he cuts them off to precise quarter inches. Considering the vast majority of wands are between 9 and 14 inches long, that allows for twenty-one distinct quarter inch measurements between 9 inches and 14 inches.

By these statistics, we can deduce that there are a total of 19,152 (38 * 3 * 8 * 21) combinations of wand wood, core, rigidity, and length commonly made by Ollivander. He can certainly make other wands, but would not in common practice.

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_{It is important to note that certain of these materials are exceedingly rare, such as Elder wood, and to a much lesser extent, Phoenix feathers. It is unlikely that Ollivander would keep a large quantity of these wands in stock, but they are still possibilities for him to make.}