Question

The number of binary strings of n zeros and k ones that no two ones are adjacent is

• A. ${}^{n+1}{C}_k$
• B. ${}^n{C}_k$
• C. ${}^n{C}_{k+1}$
• D. none of these

Answer 1

The correct option is A ${}^{n+1}{C}_k$

First arrenging all n zero in a raw. There is only 1 way for arranging n zeros in a row. By arranging n zeros in a row, we get (n+1) positions to place once.
So number of ways arranging k once in (n+1) positions= ${}^{n+1}{C}_k$
$\therefore$ Required number of binary strings of n zeros and k once that no two ones are adjacent
$=1{\times }^{n+1}{C}_k{=}^{n+1}{C}_k.$