If P(9, r) = 3024, find r. - Vidyadip

Question

If P(9, r) = 3024, find r.

✓

Answer

We have,
P(9, r) = 3024
${P}(9,\text{r}) = \frac{9!}{(9-\text{r})!}\Big[\because^\text{n}\text{P}_\text{r}=\frac{\text{n!}}{(\text{n}-\text{r})!}\Big]$
$ \Rightarrow\frac{1}{(9-\text{r})!} =\frac{3024}{9\times 8\times7\times6\times5\times4\times3\times2\times1}$
$ \Rightarrow\frac{1}{(9-\text{r})!} =\frac{336}{8\times7\times6\times5\times4\times3\times2\times1}$
$ \Rightarrow\frac{1}{(9-\text{r})!} =\frac{42}{7\times6\times5\times4\times3\times2\times1}$
$ \Rightarrow\frac{1}{(9-\text{r})!} =\frac{42}{7\times6\times5\times4\times3\times2\times1}$
$ \Rightarrow\frac{1}{(9-\text{r})!} =\frac{1}{5\times4\times3\times2\times1}$
$ \Rightarrow\frac{1}{(9-\text{r})!} =\frac{1}{5!}$
$\Rightarrow (9-\text{r})! =5!$
$\Rightarrow 9-\text{r}= 5$
$\Rightarrow 9-5=\text{r}$
$\Rightarrow 4=\text{r}$
$\Rightarrow \text{r}= 4$
Hence, $ \text{r}= 4 $

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Permutations→Permutations — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\sin3\text{x}+7\text{x}}{4\text{x}+\sin2\text{x}}$

Differentiate $\frac{\cos x}{x}$ from first principle.

Find the equation to the ellipse in the following case:

Length of major axis 16 foci $(0, \pm6)$

If $\sin\alpha=\frac{4}{5}$ and $\cos\beta=\frac{5}{13},$ prove that $\cos\frac{\alpha-\beta}{2}=\frac{8}{\sqrt{65}}$

Use the Principle of Mathematical Induction in the following Exercis.
Prove that for all $\text{n}\in\text{N},\cos\alpha+\cos(\alpha+\beta)+\cos(\alpha+2\beta)+\ ....\ +\cos\big[\alpha+(\text{n}-1)\beta\big]$$=\frac{\cos\Big[\alpha+\big(\frac{\text{n}-1}{2}\big)\beta\Big]\sin\big(\frac{\text{n}\beta}{2}\big)}{\sin\frac{\beta}{2}}$

Find the equation of a line perpendicular to the line 3x - y + 5 = 0 and at a distance of 3 units from the origin.

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
$\frac{x^2}{100}+\frac{y^2}{400}=1$

Prove the following:
$\sin(\text{n}+1)\text{x}\sin(\text{n}+2)\text{x}+2\cos(\text{n}+1)\text{x}\cos(\text{n}+2)\text{x}=\cos\text{x}$

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow1}\frac{(2\text{x}-3)\big(\sqrt{\text{x}}-1\big)}{3\text{x}^2+3\text{x}-6}$

If $\text{z}_1=2-\text{i}, \ \text{z}_2=1+\text{i},$ Find $\Big|\frac{\text{z}_1+\text{z}_2+1}{\text{z}_1-\text{z}_2+\text{i}}\Big|.$