Q. A binary sequence is an array of 0’s and 1’s. The number of $n -$digit binary sequence which contain even number of 0’s is
A) $2^{n - 1}$
B) $2^{n} - 1$
C) $2^{n - 1} - 1$
D) $2^{n}$
Explanation
(a)
The required number of ways=The even number of 0’s $ie,$ {0, 2, 4, 6, …}
$= \frac{n!}{n!} + \frac{n!}{2!(n - 2)!} + \frac{n!}{4!(n - 4)!} + \ldots$
$= \ ^{n}C_{0} + \ ^{n}C_{2} + \ ^{n}C_{4} + ... = 2^{n - 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.