Question

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

• A. $68$
• B. $68$$!$
• C. ${16}^{17}$
• D. ${68}^{68}$

Answer 1

Answer: (C)

${16}^{17}$

This problem is like there are $68$ space to be filled with $68$ things.Each space has option to get filled up or not.

The required number is equal to the number of all subsets of a $68$ elements set i.e

$\Rightarrow$ ${}^{68}{C}_0+{}^{68}{C}_1+{}^{68}{C}_2+....+{}^{68}{C}_{68}$

$\Rightarrow$ $2^{68}$

$\Rightarrow$ ${16}^{17}$

The total number of a crocodile with a different set of teeth, are ${16}^{17}.$