If A={1, 2, 3, ... , 10}, then how many subsets of A contain the element 1, but not 4?

$A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ has 10 elements total.

The subset must contain $1$ and must not contain $4$.

Element $1$: must be IN $\rightarrow$ 1 choice

Element $4$: must be OUT $\rightarrow$ 1 choice

Remaining 8 elements $(2, 3, 5, 6, 7, 8, 9, 10)$: each can be IN or OUT $\rightarrow$ 2 choices each

Total subsets $= 1 \times 1 \times 2^8$

$= 2^8$

$= 256$