Question

How many numbers exceeding $999$ and not exceeding $5000$ can be formed, such that each digit is any of the first six whole numbers?

• A. $625$
• B. $600$
• C. $865$
• D. $864$

Answer 1

The correct option is C $865$

We need to find $4$ digit numbers less than equal to $5000$ which contain only $0,1,2,3,4,5.$

The first digit (thousands digit) cannot be $0$ or $5$ since $0$ would make it a $3$ digit number $\xi$ not $5$ since number $\le 5000$

$\Rightarrow$ $1st$ digit can be any of the other $4={}^4{C}_1=4$

The $2nd,3rd$ $\xi$ $4th$ can be any of the $6$ whole numbers.

$\Rightarrow$ Total $=4\times 6\times 6\times 6=864$

$\Rightarrow$ Also including $5000$ it is $(864+1)=865.$

Hence, the answer is $865.$