\(^{4}C_2 \times ^{3}C_1\) = \(\left(\frac{4!}{(4-2)!2!}\right)\times\left(\frac{3!}{(3-1)!1!}\right)\) = \(\frac{4!}{2!2!}\times \frac{3!}{2!}\) = \(\frac{4 \times 3 \times 2!}{2 \times 1 \times 2!} \times \frac{3 \times 2!}{2!} = 18\)