Question:
If P (9, r) = 3024, find r.
Solution:
P (9, r) = 3024
$\Rightarrow \frac{9 !}{(9-r) !}=3024$
$\Rightarrow \frac{9 !}{(9-r) !}=9 \times 8 \times 7 \times 6$
$\Rightarrow \frac{9 !}{(9-r) !}=\frac{9 \times 8 \times 7 \times 6 \times 5 !}{5 !}$
$\Rightarrow \frac{9 !}{(9-r) !}=\frac{9 !}{5 !}$
$\Rightarrow(9-r) !=5 !$
$\Rightarrow 9-r=5$
$\Rightarrow r=4$
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