If ^n P_r = 720.^n C_r , then r is equal to - Vidyadip

MCQ

If $^n{P_r}$=$ 720$.$^n{C_r},$ then $r$ is equal to

✓
$6$
B
$5$
C
$4$
D
$7$

✓

Answer

Correct option: A.

$6$

a
(a) $^n{P_r}\, = 720.{\,^n}{C_r}$

==> $^n{P_r}\, \div {\,^n}{C_r}\, = 720$

==> $\,r\,! = 720 = 6\,!$

$==> r = 6.$

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 "MCQ" from permutation and combination→permutation and combination — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\mathop {\lim }\limits_{x \to 1} {\sin ^{ - 1}}\left( {\frac{k}{{\ln x}} - \frac{k}{{x - 1}}} \right)$ exist, then the number of integers in the range of $k$ , is

The co-ordinates of three points $A(-4, 0) ; B(2, 1)$ and $C(3, 1)$ determine the vertices of an equilateral trapezium $ABCD$ . The co-ordinates of the vertex $D$ are :

The equation of a common tangent to the parabolas $y = x ^{2}$ and $y =-( x -2)^{2}$ is.

Let $S$ be the set of all passwords which are six to eight characters long, where each character is either an alphabet from $\{ A , B , C , D , E \}$ or a number from $\{1,2,3,4,5\}$ with the repetition of characters allowed. If the number of passwords in $S$ whose at least one character is a number from $\{1,2,3,4,5\}$ is $\alpha \times 5^{6}$, then $\alpha$ is equal to $.......$

A bag contains $3$ red and $7$ black balls, two balls are taken out at random, without replacement. If the first ball taken out is red, then what is the probability that the second taken out ball is also red

The sum of all the elements in the set $\{\mathrm{n} \in\{1,2, \ldots \ldots ., 100\} \mid$ $H.C.F.$ of $n$ and $2040$ is $1\,\}$ is equal to $.....$

If ${({a^m})^n} = {a^{{m^n}}}$, then the value of $'m'$ in terms of $'n'$ is

If $a,\;b,\;c$ are ${p^{th}},\;{q^{th}}$ and ${r^{th}}$ terms of a $G.P.$, then ${\left( {\frac{c}{b}} \right)^p}{\left( {\frac{b}{a}} \right)^r}{\left( {\frac{a}{c}} \right)^q}$ is equal to

The length of the latus rectum of a parabola, whose vertex and focus are on the positive $x$-axis at a distance $\mathrm{R}$ and $\mathrm{S}(\,>\,\mathrm{R})$ respectively from the origin, is:

Number of integral solutions satisfy inequality $|\text{x-3}|-|2\text{x}+5|\geq|\text{x}+8|$