Choose the correct answer. The total number of 9 digit numbers wh… - Vidyadip

MCQ

Choose the correct answer. The total number of 9 digit numbers which have all different digits is.

A
10!
B
9 !
✓
9 × 9!
D
10×10!

✓

Answer

Correct option: C.

9 × 9!

9 × 9!

Solution:
We have to form 9-digit number which has all different digit.
First digit from the left can be filled in 9 ways (excluding ' 0 ').
Now nine digits are left including ' O '.
So remaining eight places can be filled with these nine digits in ${ }^9 \mathrm{P}_5$ ways.
So, total number of numbers $=9 \times{ }^9 \mathrm{P}_8=9 \times 9!$

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 PERMUTATIONS AND COMBINATIONS→PERMUTATIONS AND COMBINATIONS — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The complete set of values of $k$, for which the quadratic equation $x^2-k x+k+2=0$ has equal roots, consists of:

The centre of the circle $x = - 1 + 2\cos \theta $, $y = 3 + 2\sin \theta $, is

If the point of intersections of the ellipse $\frac{ x ^{2}}{16}+\frac{ y ^{2}}{ b ^{2}}=1$ and the circle $x ^{2}+ y ^{2}=4 b , b > 4$ lie on the curve $y^{2}=3 x^{2},$ then $b$ is equal to:

The number of real values of $\lambda$ for which the lines $\text{x} - 2\text{y} + 3 = 0, \lambda\text{x} + 3\text{y} + 1 = 0$ and $4\text{x} - \lambda\text{y} + 2 = 0$ are concurrent is:

Solve: $|\text{x}-1|\leq 5, |\text{x}|\geq2$

${\left( {\frac{{\cos A + \cos B}}{{\sin A - \sin B}}} \right)^n} + {\left( {\frac{{\sin A + \sin B}}{{\cos A - \cos B}}} \right)^n}$ $(n$ even or odd$) =$

If $\sin(\text{B+C}-\text{A}),\sin(\text{C+A}-\text{B}),\sin(\text{A+B}-\text{C})$ are in A.P., than $\cot\text{A},\cot\text{B},\cot\text{C}$ are in

If $\sin \beta $ is the geometric mean between $\sin \alpha $ and $\cos \alpha ,$ then $\cos 2\beta $ is equal to

The probability that a leap year will have $53$ Fridays or $53$ Saturdays is

The equation of the straight line which passes through the point (-4, 3) such that the portion of the line between the axes is divided internally by the point in the ratio 5 : 3 is: