A five - digit number is written down at raddom. The probability … - Vidyadip

MCQ

A five $-$ digit number is written down at raddom. The probability that the number is divisible by $5,$ and no two consecutive digits are identical, is :

A
$\frac{1}{5}$
B
$\frac{1}{5}\big(\frac{9}{10}\big)^3$
C
$\big(\frac{3}{5}\big)^4$
✓
None of these

✓

Answer

Correct option: D.

None of these

If last digit is either $O$ or $5$ then the number is divisible by $5.$
Case : $1$
Last digit is $0.$
First three places can be selected by $9 \times 9 \times 9 = 729$ ways.
If $c = 0 $ then three places can be selected by $9 \times 8 \times 1 = 72$
If $C \neq 0$ then $729 - 72 = 657$
Fourth place has $8$ choices $= 657 \times 8 = 5256$
Total $= 72 + 5256 = 5904$
Case : $2$
If $C = 5$
First place other than $5$
then first three places can be filled in $8 \times 8 \times 1 = 64$
If first place is $5$ then first three places can be filled in $1\times 9 \times 1 = 9 $ ways.
If third place is other than $5$ then $729 - 64 - 9 = 656$ ways.
For fourth place has $8$ choices.
As per required condition $= (64 + 9) \times 9 + 656 \times 8 = 5905$
required probability $=\frac{5904+5905}{9\times10\times10\times10\times10}=\frac{11809}{90000}$
Note : Answer not matching with back answer.

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 "M.C.Q (1 Marks)" from Probability→Probability — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let ${a_2},{a_3} \in R$ such that $\left| {{a_2} - {a_3}} \right| = 6$ and $f\left( x \right) = \left| {\begin{array}{*{20}{c}}
1&{{a_3}}&{{a_2}}\\
1&{{a_3}}&{2{a_2} - x}\\
1&{2{a_3} - x}&{{a_2}}
\end{array}} \right|,x \in R.$ Then the greatest value of $f(x)$ is

The solution of the differention equation $(1+\text{x}^{2})\frac{\text{dy}}{\text{dx}}+1+\text{y}^{2}=0$ is:

The number of real values of $x$ at which the function $f(x)=\left|\begin{array}{ccc}1 & |x| & x^2 \\1 & |x-1| & (x-1)^2 \\1 & |x-2| & (x-2)^2\end{array}\right|$is not differentiable is

If $\text{y}=\sqrt{\sin\text{x}+\text{y}},$ then $\frac{\text{dy}}{\text{dx}}$ equals:

If $P(A)=0.4, P(B)=0.8$ and $P(B \mid A)=0.6$, then $P(A \cup B)$ is equal to

Let $\vec{\text{a}}=\text{a}_1\hat{\text{i}}+\text{a}_2\hat{\text{j}}+\text{a}_3\hat{\text{k}},\vec{\text{b}}=\text{b}_1\hat{\text{i}}+\text{b}_2\hat{\text{j}}+\text{b}_3\hat{\text{k}}$ and $\vec{\text{c}}=\text{c}_1\hat{\text{i}}+\text{c}_2\hat{\text{j}}+\text{c}_3\hat{\text{k}}$ be three zero vectors such that $\vec{\text{c}}$ is a unit vector perpendicular to both $\vec{\text{a}}$ and $\vec{\text{b}}.$ If the angle between $\vec{\text{a}}$ and $\vec{\text{b}}$ is $\frac{\pi}{6},$ then $\begin{vmatrix}\text{a}_1&\text{a}_2&\text{a}_3\\\text{b}_1&\text{b}_2&\text{b}_3\\\text{c}_1&\text{c}_2&\text{c}_3 \end{vmatrix}^2$ is equal to :

Choose the correct answer from the given four options.If $\text{P}(\text{A})=0.4,\text{P}(\text{B})=0.8$ and $\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)=0.6,$ then $\text{P}(\text{A}\cup\text{B})$ is equal to:

If points $\text{A}(60\hat{\text{i}}+3\hat{\text{j}}),\ \text{B}(40\hat{\text{i}}-8\hat{\text{j}})$ and $\text{C}(\text{a}\hat{\text{i}}+52\hat{\text{j}})$ are collinear, then a is equal to,

$\int_{}^{} {\frac{1}{{(x - 1)({x^2} + 1)}}dx} = $

Line passing through $(3, 4, 5)$ and $(4, 5, 6)$ has direction ratios: