Question

If ¹²P_r = 1320, then r =__________.

Answer 1

Given ¹²P_r = 1320
$$\begin{gathered} \mathrm{i}.\mathrm{e}\frac{12!}{\left(12-r\right)!}=1320 \\ \Rightarrow \left(12-r\right)!=\frac{12!}{1320} \\ \Rightarrow \left(12-r\right)!=\frac{12\times 11\times 10\times 9!}{12\times 11\times 10} \\ \Rightarrow \left(12-r\right)!=9! \\ \Rightarrow 12-r=9 \\ \Rightarrow r=12-9 \\ \mathrm{i}.\mathrm{e}r=3 \end{gathered}$$