How many bit strings of length 8 have at least twice as many 0’s as 1’s?

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A problem on my discrete mathematics homework.

My thought process is as follows: For there to be at least twice as many 0's as 1's, there can only be at most, 2 1's.

Total possible strings: $2^8 = 256$

Exactly 2 1's $= C(8, 2) = 28$

Exactly 1 1's $= 8$

Does that mean that for there to be at least twice as many 0's as 1's, I would have $8+28$ possible strings, leaving $36$ total?