First slide

Combinations

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, the maximum population of the city is

Moderate

A

2³²
B

(32)²-1
C

2³²-1
D

2³²-1

Solution

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 2³². As there is no person without a tooth, the maximum population is 2³²- 1.

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