A majority of ones

Among all binary strings of length $6$ , how many contain strictly more $1$ 's than $0$ 's?

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Remove the tied ( $3$ – $3$ ) strings first, then split the rest by $0\leftrightarrow 1$ symmetry.
$(2^6 - \binom{6}{3})/2$ .

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Asked at: Probability & Market-Making, Mixed Quant & Coding