Subsets of 1 to 10 with two of the first three

Count the subsets of $\{1,2,\dots,10\}$ that include exactly two of the numbers $1$, $2$, $3$.

$384$. Choose which two of $\{1,2,3\}$ appear ($\binom32=3$ ways), then each of the other seven numbers is freely in or out ($2^7=128$ ways): $3\cdot128=384$.