Question

If ${}^{16}{C}_r{=}^{16}{C}_{r+1}$, then the value of ${}^r{P}_{r-3}$ is

• A. 31
• B. 120
• C. 210
• D. 840
• E. No option is correct

Answer 1

The correct option is E No option is correct

${}^{16}{C}_r{=}^{16}{C}_{r+1}$

$\Rightarrow {}^{16}{C}_{16-r}{=}^{16}{C}_{r+1}(\because {}^n{C}_{n-r})$

$\Rightarrow 16-r=r+1$
$\Rightarrow 2r=15$

$\Rightarrow r=7.5$

Which is not possible, since r should be an integer.