Question:
If nPr = 840 and nCr = 35, then r = ___________.
Solution:
Given nPr = 840 and nCr = 35
i. e $\frac{n !}{(n-r) !}=840$ and $\frac{n !}{r !(n-r) !}=35$
$\therefore\left(\frac{n !}{(n-r) !}\right) \frac{1}{r !}=35$
i. e $840\left(\frac{1}{r !}\right)=35 \quad\left(\because \frac{n !}{(n-r) !}=840\right.$ given $)$
i. e $r !=\frac{840}{35}=24$
$=4 \times 3 \times 2$
$=4 !$
i.e $r=4$