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How many binary sequences of length 7 have at least two 1's? Can someone please explain the procedure in detail please. I tried solving it using the "count what you do not want" procedure, but I got nowhere. Thank you in advance

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    $\begingroup$ What do you get if you count those that have exactly zero or exactly one 1? $\endgroup$ – fuglede Feb 9 '15 at 17:16
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The number of $7$-digit sequences is $2^7=128$

The number of $7$-digit sequences with $0$ occurrences of "one" is $\binom70=1$

The number of $7$-digit sequences with $1$ occurrence of "one" is $\binom71=7$

The number of $7$-digit sequences with $2$ or more occurrences of "one" is $128-(1+7)=120$

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  • $\begingroup$ @MathLover95: You're welcome :) $\endgroup$ – barak manos Feb 9 '15 at 18:43

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