i have actually this question however i don"t understand the price please assist me: How countless bit strings of size 12 save at least three 1 s and at the very least three 0 s?

There are \$2^12=4096\$ little strings altogeher. That these, the variety of bit strings containing specifically 0,1 or 2 1"s is \$\$12choose 0+12choose 1+12choose 2=1+12+66=79\$\$Similarly, the variety of bit strings containing specifically 0,1 or 2 0"s is likewise 79. Over there is no overlap. Thenumber of little strings satisfying the problem is 4096 - 2 \$ imes\$79=4096-158=3938.

The means to ar only 2 "ones" (remaining gift "zeros") room \$inom 122\$, and \$inom121, inom120\$ those that placing only one and also none.Same for the "zeros".

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Taking out from the full \$2^12= inom 120+ inom 121+ cdots\$ the over two tails offers the answer.

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