AP EAMCET · Maths · Permutation Combination
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
- A \(2^{n-1}\)
- B \(2^n-1\)
- C \(2^{n-1}-1\)
- D $2^n
Answer & Solution
Correct Answer
(A) \(2^{n-1}\)
Step-by-step Solution
Detailed explanation
The required number of ways \(=\) The even number of 0 's ie, \(\{0,2,4,6, \ldots\}\) \(\begin{aligned} & =\frac{n !}{n !}+\frac{n !}{2 !(n-2) !}+\frac{n !}{4 !(n-4) !} \\ & ={ }^n C_0+{ }^n C_2+{ }^n C_4+\ldots=2^{n-1} \end{aligned}\)
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