Question

The number of $4$ digits numbers which do not contain $4$ different digit is?

• A. $2432$
• B. $3616$
• C. $4210$
• D. $4464$

Answer 1

The correct option is D

$4464$

Step 1: Find the total number of possible numbers when repetition is not allowed

Total no of digit is $10$

In the first place we cannot have $0$.

So the possible no of choice is $9$

In the second place we can have $0$ and we cannot repeat any digit

So the possible no of choice is $9$

In the third place we can have $0$ and we cannot repeat any digit

So the possible no of choice is $8$

In the third place we can have $0$ and we cannot repeat any digit

So the possible no of choice is $7$

Total number of numbers when repetition is not allowed $=9\times 9\times 8\times 7=4536$

Step 2: Find the total number of possible numbers which do not contain different digits.

Total number of $4$ digit number which can be formed is $9\times 10\times 10\times 10=9000$

Therefore total number of numbers which doesn't contain $4$ different digits is $=9000-4536=4464$

Hence, the correct option is $\left(\mathrm{D}\right)$.