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, the maximum population of the city is a. `2^(32)` b. `(32)^2-1` c. `2^(32)-1` d. `2^(32-1)`

Options

A. `2^(32)`
B. `2^(32)+1`
C. `2^(32)-1`
D. `2^(32)-2`

Answer

C

Explanation

There are `32` places for the teeth in the mouth for each place we have two choices either there is a tooth or there is on tooth.
`implies` choices of `32` teeth `e=2^(32)`
which include without teeth (each choice has no tooth)
but given no person without a tooth
`implies` maximum population of the city `=2^(32)-1`