First slide

Permutations

Question

If $E = \frac{1}{4} \cdot \frac{2}{6} \cdot \frac{3}{8} \cdot \frac{4}{10} \dots \frac{30}{62} \cdot \frac{31}{64} = 8^{x}$ , then value of $x$ is

Moderate

A

-7
B

-9
C

-10
D

-12

Solution

We have
$E = \frac{31!}{2^{31} (32!)} = \frac{1}{2^{31} (32)} = \frac{1}{2^{36}} = 2^{- 36} = {(2^{3})}^{- 12} = 8^{- 12}$
Thus, $x = - 12$

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