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 "Solve the Following Question.(4 Marks)" from Permutations→Permutations — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the value of

$x^3+x^2-x+22$, if $x=\frac{5}{1-2 i}$

Differentiate the following from first principle:$\sqrt{2\text{x}^2-1}$

Solve the following system of equations in R.
$\Big|\frac{3\text{x}-4}{2}\Big|\leq\frac{5}{12}$

If $5^{th}, 8^{th}$ and $11^{th}$ term of G.P. are $p, q$ and $s$ respectively, prove that $q^2 = ps$.

Discuss the continuity of the following functions at the points indicated against them. $\begin{aligned} f(x) & =\frac{\sqrt{3}-\tan x}{\pi-3 x}, x \neq \frac{\pi}{3} \\ & =\frac{3}{4}, \quad \text { for } x=\frac{\pi}{3}, \text { at } x=\frac{\pi}{3} .\end{aligned}$

The odds against a husband who is 60 years old, living till he is 85 are 7 : 5. The odds against his wife who is now 56, living till she is 81 are 5 : 3. Find the probability that : (i) at least one of them will be alive 25 years hence. (ii)exactly one of them will be alive 25 years hence.

Find Sn of the following arithmetico-geometric sequences.

$2,4 x, 6 x^2, 8 x^3, 10 x^4, \ldots \ldots$

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow-\infty}\big(\sqrt{\text{x}^2-8\text{x}}+\text{x}\big)$

For any two sets A and B, prove that: $\text{A}\cap\text{B}=\phi\Rightarrow\text{A}\subseteq\text{B}'.$

Prove that:
$\cos\frac{\pi}{15}\cos\frac{2\pi}{15}\cos\frac{4\pi}{15}\cos\frac{7\pi}{15}=\frac{1}{16}$