Question

Find the indicated values. (Permutations and combinations.)

(a) yPy − 2

(b) yCy − 2

Answer 1

`\bf _nP_r=\cfrac{n!}{(n-r)!}~\hspace{10em}_yP_y=\cfrac{y!}{(y-y)!}\implies _yP_y=\cfrac{y!}{0!} \\\\\\ _yP_y=\cfrac{y!}{1}\implies _yP_y=y!~\hspace{9em}_yP_y-2\implies \boxed{y!-2} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ _nC_r=\cfrac{n!}{r!(n-r)!}~\hspace{10em}_yC_y=\cfrac{y!}{y!(y-y)!}\implies _yC_y=\cfrac{y!}{y!0!} \\\\\\ _yC_y=\cfrac{y!}{y!\cdot 1}\implies _yC_y=1~\hspace{7em}_yC_y-2\implies 1-2\implies \boxed{-1}`