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Question

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

A
n+1Ck
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B
nCk
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C
nCk+1
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D
none of these
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Solution

## The correct option is A n+1CkFirst 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+1Ck ∴ Required number of binary strings of n zeros and k once that no two ones are adjacent =1×n+1Ck=n+1Ck.

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