First slide

Combinations

Question

A crocodile is known to have not more than 68 teeth. The total number of crocodiles with different set of teeth is

Moderate

A

68
B

68!
C

16¹⁷
D

68⁶⁸

Solution

The required number is equal to the number of all the subsets of a 68 elements set i.e.,
$68_{C_{0}} + 68_{C_{1}} + 68_{C_{2}} + \dots + 68_{C_{68}} = 2^{68} = 16^{17}$

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