# How many binary sequences of length 7 have at least two 1's?

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

• What do you get if you count those that have exactly zero or exactly one 1? – fuglede Feb 9 '15 at 17:16

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 $128-(1+7)=120$