A five digit number is formed by writing the digits 1, 2, 3, 4, 5… - Vidyadip

MCQ

A five digit number is formed by writing the digits $1, 2, 3, 4, 5$ in a random order without repetitions. Then the probability that the number is divisible by $4$ is

A
$\frac{3}{5}$
B
$\frac{{18}}{5}$
✓
$\frac{1}{5}$
D
$\frac{6}{5}$

✓

Answer

Correct option: C.

$\frac{1}{5}$

c
(c) The number is divisible by $4$ if last two digits are $12, 24, 32$ and $52$. Remaining three places can be filled by $3!$ ways.
$\therefore $ Favouable cases = $3\,!\,\, \times \,\,4$
Required probability = $\frac{{3\,!\,\, \times 4}}{{5!}} = \frac{1}{5}$.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A variable chord is drawn through the origin to the circle ${x^2} + {y^2} - 2ax = 0$. The locus of the centre of the circle drawn on this chord as diameter, is

If $f(x)=\left\{\begin{array}{cc}x^3 \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array}\right.$, then

If an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces, is through five times, then the probability that the product of the outcomes is positive, is :

Let $f(x)=\int_0^{x^2} \frac{t^2-8 t+15}{e^t} d t, x \in R$. Then the numbers of local maximum and local minimum points of $f$, respectively, are :

$\int_{}^{} {\frac{{3\sin x + 2\cos x}}{{3\cos x + 2\sin x}}\;dx = } $

The value of $\frac{{{{\sin }^2}\theta }}{{\sin \theta - \cos \theta }} - \frac{{\sin \theta + \cos \theta }}{{{{\tan }^2}\theta - 1}}$ for all permissible vlaues of $\theta$

If $y = {x^2}{e^{mx}}$, where $m$ is a constant, then ${{{d^3}y} \over {d{x^3}}} = $

Let $R = \{(a, a)\}$ be a relation on a set $A$. Then $R$ is

If $f(x) = {\cos ^2}x + {\sec ^2}x,$ then

What is the sum of the coefficients of ${({x^2} - x - 1)^{99}}$