A box contains coupons labelled 1,2, , 100. Five coupons are pick… - Vidyadip

MCQ

A box contains coupons labelled $1,2, \ldots, 100$. Five coupons are picked at random one after another without replacement. Let the numbers on the coupons be $x_1, x_2, \ldots, x_5$. What is the probability that $x_1 > x_2 > x_3$ and $x _3 < x _4 < x _5 ?$

A
$1 / 120$
B
$1 / 60$
✓
$1 / 20$
D
$1 / 10$

✓

Answer

Correct option: C.

$1 / 20$

c
(c)

We have,$100$ coupons labelled $1$ , $2,3, \ldots 100$

Five coupons are random selected and arranged.

$\therefore$ Total numbers of outcomes $={ }^{110} C_5 \times 5$ !

Five coupons $x_1, x_2, x_3, x_4, x_5$ are arranged such that $x_1 > x_2 > x_3$ and

$x_3 < x_4 < x_5$

Favourable outcomes $={ }^{100} C_5 \times \frac{4 !}{2 ! 2 !}$

$\therefore \text { Required probability } =\frac{{ }^{100} C_5 \times \frac{4 !}{2 ! 2 !}}{{ }^{100} C_5 \times 5 !}$

$=\frac{1}{20}$

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 14. probability→14. probability — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The locus represented by $|z - 1| = |z + i|$ is

If $A$ and $B$ are two given sets, then $A \cap {(A \cap B)^c}$ is equal to

Consider a hyperbola $\mathrm{H}$ having centre at the origin and foci and the $\mathrm{x}$-axis. Let $\mathrm{C}_1$ be the circle touching the hyperbola $\mathrm{H}$ and having the centre at the origin. Let $\mathrm{C}_2$ be the circle touching the hyperbola $\mathrm{H}$ at its vertex and having the centre at one of its foci. If areas (in sq. units) of $\mathrm{C}_1$ and $\mathrm{C}_2$ are $36 \pi$ and $4 \pi$, respectively, then the length (in units) of latus rectum of $\mathrm{H}$ is

If the fourth term of the binomial expansion of $\Big(\text{px}+\big(\frac{1}{\text{x}}\big)\Big)^\text{n}$ is $\frac{5}{2},$ then:

The number of non-zero integral solutions of the equation $|1 - i{|^x} = {2^x}$ is

If complex numbers $z_1$ and $z_2$ both satisfy $z + \overline z = 2 | z -1 |$ and $arg(z_1 -z_2) = \frac{\pi}{3} ,$ then value of $Im (z_1 + z_2)$ is, where $Im (z)$ denotes imaginary part of $z$ -

The equation of the circle passing through the point $(1,1)$ and having two diameters along the pair of lines $x^2-y^2-$ $2 x+4 y-3=0$, is:

Equation of a circle whose centre is origin and radius is equal to the distance between the lines $x = 1$ and $x = - 1$ is

A box contains $2$ black, $4$ white and $3$ red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box, another ball is drawn at random and kept aside the first. This process is repeated till all the balls are drawn from the box. The probability that the balls drawn are in the sequence of $2$ black, $4$ white and $3$ red is

Solution of $2\text{x}-\frac{3}{3\text{x}}-5\geq3$ is: