Question

In a city no two persons have identical set of teeth and there is no person without a tooth. Also no person has more than 32 teeth. If we disregard the shape and size of tooth and consider only the positioning of the teeth, then the maximum population of the city

• A. $2^{32}$
• B. $2^{32}$
• C. $2^{32}$ - 1
• D. $2^{32-1}$

Answer 1

The correct option is C

$2^{32}$ - 1

We have 32 places for teeth. For each place we have two choices either there is a tooth or there is no tooth. Therefore the number of ways to fill up these places is $2^{32}$. As there is no person without a tooth, the maximum population is $2^{32}-1$.