# How many combinations exist?

How many combinations exist between this range of lowercase hex values: b000000000000000 to bfffffffffffffff?

If it was just 0000000000000000 to ffffffffffffffff, then it would be $$16^{16}$$,right?

My thought would be $$16^{16}-16^{15}$$, but I do not know if that is correct?

• No, it is not. You can just ignore the leading b's. Consider in decimal how many numbers between 200 and 299. The leading 2's do not matter. You also need to define whether you count either or both ends for there to be an answer. Commented Jan 14, 2023 at 14:19

You are looking for the amount of combinations that exist for a word of $$15$$ letters with an alphabet of $$16$$ letters. If we calculate $$\left(BFFFFFFFFFFFFFFF\right)_{16} - \left(B000000000000000\right)_{16}$$ = $$\left(FFFFFFFFFFFFFFF\right)_{16}$$ one can see that the leading B wont change the amount of combinations. If we now convert this number into decimal form we get: $$\left(FFFFFFFFFFFFFFF\right)_{16} = \left(1\;152\;921\;504\;606\;846\;975\right)_{10}$$. This is the maximum number we can display; Including the Zero there has to be $$\left(1\;152\;921\;504\;606\;846\;976\right)_{10}$$ combinations which is equal to your Base $$B = 16$$ to the power of the amount of letters $$L = 15$$: $$B^L = 16^{15} = \left(1\;152\;921\;504\;606\;846\;976\right)_{10}$$