A business has 9 applicants for 2 job openings, one as a manager and another as just a regular employee. How many ways can the business select 2 new employees out of the 9 candidates?
To find the number of ways 2 new employees can be selected from a group of 9 candidates,
\[\begin{align*} {}_9P_2 &= \frac{9!}{(9-2)!} \\ &= \frac{9!}{7!} \\ &= \frac{9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{~~~~~~~~~~~~~~7\times 6\times 5\times 4\times 3\times 2\times 1} \\ &= 9\times 8 \\ &= \mathbf{72} \end{align*}\]