Question

The domain of ${{}^{9-x}P}_{x-2}$ is

• A. $x\in \{2,3,4,5,6\}$
• B. $x\in \{2,3,4,5\}$
• C. $x\in \{3,4,5\}$
• D. $x\in \{3,4,5,6\}$

Answer 1

The correct option is B $x\in \{2,3,4,5\}$

We know that for ${{}^{n}P}_r,$
$n>0,r\ge 0,n\ge r\&n,r\in I$

For ${{}^{9-x}P}_{x-2},$ we have
$9-x>0,x-2\ge 0,9-x\ge x-2$
$\Rightarrow x<9,x\ge 2,x\le \frac{11}{2}$
$\Rightarrow x\ge 2\&x\le \frac{11}{2}$
$\Rightarrow x\in \{2,3,4,5\}$