Question

$C_{6} ^{2}$ - $A_{4} ^{2}$

Answer 1

$C^{k}_{n} = \frac{n!}{k!(n-k)!}, \text{ } A^{k}_{n} = \frac{n!}{k!}$

$C^{2}_{6} - A^{2}_{4} = \frac{6!}{2! \cdot 4!} - \frac{4!}{2!} = \frac{6 \cdot 5 \cdot 4!}{2! \cdot 4!} - \frac{4\cdot 3 \cdot 2!}{2!} = 15 - 12 = \boxed{3}$