Q46 / 160 · AP EAMCET 2009 · Mathematics
A binary sequence is an array of 0's and 1's. The number of $n$-digit binary sequences which contain even number of 0's is
- Correct answerA$2^{n-1}$
- B$2^n-1$
- C$2^{n-1}-1$
- D$2^n
Solution
The required number of ways $=$ The even number of 0 's ie, $\{0,2,4,6, \ldots\}$
$\begin{aligned}
& =\frac{n !}{n !}+\frac{n !}{2 !(n-2) !}+\frac{n !}{4 !(n-4) !} \\
& ={ }^n C_0+{ }^n C_2+{ }^n C_4+\ldots=2^{n-1}
\end{aligned}$
Hence, the correct answer is option: 'A'.