There are "12 choose 5" or 12C5 ways to select any 5 TV sets.
From this number we must subtract:
(1). the number of selections of 5 that contain no defective TV sets
as well as
(2). the number of selections of 5 that contain only 1 defective TV set.
We calculate (1) and (2)
(1). Choices of 5 with no defective TV sets:
Since there are 12 sets and 3 are defective, there are 12-3 or 9
non-defective ones, so this is "9 choose 5", or 9C5.
(2). Choices of 5 with 4 non-defective sets and 1 defective set:
"9 choose 4" times "3 Choose 1" or (9C4)(3C1)
Subtracting the number of choices of (1) and (2), which do not contain
at least 2 defective TVs from the total number of choices of any 5
TVs, we have:
12C5 - 9C5 - (9C4)(3C1)
792 - 126 - (126)(3) = 288
That's the answer, 288.
Edwin
