Word ‘UNIVERSITY’ is arranged randomly. Then the probability that… - Vidyadip

MCQ

Word ‘$UNIVERSITY$’ is arranged randomly. Then the probability that both ‘$I$’ does not come together, is

A
$\frac{3}{5}$
B
$\frac{2}{5}$
✓
$\frac{4}{5}$
D
$\frac{1}{5}$

✓

Answer

Correct option: C.

$\frac{4}{5}$

c
(c) Total number of ways $ = \frac{{10\,!}}{{2\,!}}$

Favourable number of ways for $'I'$ come together is $9\,!$

Thus probability that $'I'$ come together

$ = \frac{{9\,!\, \times \,2\,!}}{{10\,!}} = \frac{2}{{10}} = \frac{1}{5}$.

Hence required probability $ = 1 - \frac{1}{5} = \frac{4}{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

If the lines $x\,=\,ay\,+\,b,\,\,z\,=\,cy\,+\,d$ and $x\, = \,a\,'z + \,b\,',\,\,y = \,c\,'z\, + \,d\,'$ are perpendicular, then

The set of all values of $\lambda$ for which the equation $\cos ^2 2 x-2 \sin ^4 x-2 \cos ^2 x=\lambda$

If $\alpha ,$ $\beta$ are different values of $x$ satisfying $a\cos x + b\sin x = c,$ then $\tan {\rm{ }}\left( {\frac{{\alpha + \beta }}{2}} \right) = $

$\int {(\sqrt {\tan x} + \sqrt {\cot x} )} $ is equal to-

The degree of the differential equation $\frac{{{d^2}y}}{{d{x^2}}} + 3{\left[ {\frac{{dy}}{{dx}}} \right]^2} = {x^2}\log \left[ {\frac{{{d^2}y}}{{d{x^2}}}} \right]$ is

The number of the real roots of the equation $(x+1)^{2}+|x-5|=\frac{27}{4}$ is ....... .

Let $A=\left\{a_{i}\right\}$ be a $3 \times 3$ matrix, where $a_{i j}=\left\{\begin{aligned}(-1)^{j-i} & \text { if } i < j \\ 2 & \text { if } i=j \$-1)^{i+j} & \text { if } i > j \end{aligned}\right.$ then $\operatorname{det}\left(3 \operatorname{Adj}\left(2 \mathrm{~A}^{-1}\right)\right)$ is equal to $.....$

The centre of the conic represented by the equation $2{x^2} - 72xy + 23{y^2} - 4x - 28y - 48 = 0$ is

Let $a, b$ and $ c $ be vectors with magnitudes $3, 4$ and $5$ respectively and $a + b + c = 0, $ then the values of $ a.b + b.c + c.a$ is

Let the coefficients of the middle terms in the expansion of $\left(\frac{1}{\sqrt{6}}+\beta x\right)^{4},(1-3 \beta x)^{2}$ and $\left(1-\frac{\beta}{2} x\right)^{6}, \beta>0$, respectively form the first three terms of an $A.P.$ If $d$ is the common difference of this $A.P.$, then $50-\frac{2 d}{\beta^{2}}$ is equal to.