Q54

Consider a digital logic circuit consisting of three $2$-to-$1$ multiplexers $\text{M1, M2}$, and $\text{M3}$ as shown below. $\mathrm{X} 1$ and $\mathrm{X} 2$ are inputs of $\mathrm{M} 1$. $\text{X3}$ and $\text{X4}$ are inputs of $\text{M2}$. $\text{A, B}$, and $\text{C}$ are select lines of $\text{M1, M2}$, and $\text{M3}$, respectively.

For an instance of inputs $\mathbf{X} \mathbf{1}=\mathbf{1}, \mathbf{X} \mathbf{2}=\mathbf{1}, \mathbf{X} \mathbf{3}=\mathbf{0}$, and $\mathbf{X} \mathbf{4}=\mathbf{0}$, the number of combinations of $\mathrm{A}, \mathrm{B}, \mathrm{C}$ that give the output $\mathbf{Y}=\mathbf{1}$ is ____________.