Question

Evaluate the expression: 16P4A. 1,820B. 10,920C. 7,280D. 43,680

Answer 1

The permutation is defined as:

$_nP_r=\frac{n!}{(n-r)!}$

Then in this case we have:

$\begin{gathered} _{16}P_4=\frac{16!}{(16-4)!} \\ =\frac{16!}{12!} \\ =\frac{16\cdot15\cdot14\cdot13\cdot12!}{12!} \\ =16\cdot15\cdot14\cdot13 \\ =43680 \end{gathered}$

Therefore the answer is D.