Question

if 10pr=720 then r = ?

Answer 1

$^{10}P_{r} =720\\ \\ \Rightarrow \frac{10!}{(10-r)!}=720 \\ \\ \Rightarrow \frac{10!}{720}= (10-r)! \\ \\ \Rightarrow \frac{10!}{6!}= (10-r)!\\ \\ \Rightarrow 7 \times 8 \times 9 \times 10= (10-r)! \\ \\ \Rightarrow 7 \times (2 \times 4) \times (3 \times 3 \times 2 \times 5) = (10-r)! \\ \\ \Rightarrow 2 \times 3 \times 4 \times 5 \times 6 \times 7= (10-r)! \\ \\ \Rightarrow 7!= (10-r)! \\ \\ \Rightarrow 7= 10-r \\ \\ \Rightarrow r = 10 - 7 \\ \\ \Rightarrow \boxed{r=3}$

Answer 2

Answer:

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