Question

How many numbers lying between $999$and $10000$can be formed with the help of the digits $0,2,3,6,7,8$ when the digits are not repeated?

• A. $100$
• B. $200$
• C. $300$
• D. $400$

Answer 1

The correct option is C

$300$

Step1. Calculate the possible number of ways for each place :

Given digits are $0,2,3,6,7,8$.

We have to form the number lying between $999$and $10000$.

Ten thousand places can be filled by $2,3,6,7,8$.

Therefore, only $5$digits can be used in the unit place.

Now, one more of these digits is placed in the hundreds place. so we are left with a total $4$ more digits as repetition of digits is not allowed.

Now, any of the left digits can be placed in the tens place.

So, the number of ways in which tens place can be filled $$=4$$
Now, one more of these digits is placed at the tens place so we are left with a total $3$ more digits as repetition of digits is not allowed.

Now, any of the left digits can be placed in one place

So, the number of ways in which one place can be filled $$=3$$

Step2. Find the total numbers :

Total number which can be formed using the digits = number of the digit at thousands place $\times$ number of the digit at hundreds place $\times$ number of the digit at tens place $\times$ number of the digit at one place

Total number which can be formed using the digits $$=5\times 5\times 4\times 3$$
Total number which can be formed using the digits $$=300$$

Thus the total numbers between $$999$$and $$10000$$are $$300$$.

Hence, the correct option is (C).