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In a city no person has 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 is

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2³²

2³² – 1

2³² + 1

None of these

answer is B.

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Detailed Solution

In the mouth, there are 32 places for the teeth. For each place, two choices are possible, i.e., either tooth or not.

Choices for 1 teeth = 2

Similarly choices for 2 teeth = 2 × 2 = 2²

Choices for 3 teeth = 2 × 2 × 2 = 2³

……………………………………..

Hence, choices for 32 teeth = 2³²

But this includes one case where there is no teeth.

∴ Required number of ways = 2³² – 1.

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