10^Pr = 5040 find out r.

\(^{10} {P}_{{r}}=5040 \\ \frac{10 !}{(10-{r}) !}=5040\left[10 {P}_{{r}}=\frac{10 !}{(10-{r}) !} \text { from }{ }^{{n}} {P}_{{r}}=\frac{{n} !}{({n}-{r}) !}\right] \\ =(10-{r}) !=\frac{10 !}{5040} \\ =\frac{10 \times 9 \times 8 \times 7 \times 6 !}{7 \times 720}[6 !=720] \\ =\frac{10 \times 9 \times 8 \times 7 \times 720}{7 \times 720} \\ =720 \\ (10-{r}) !=6 ! \\ 10-{r}=6 \\ {r}=10-6\\ {r}=4\)

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