Question

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

• A. $100$
• B. $600$
• C. $300$
• D. $400$

Answer 1

The correct option is C

$300$

Analyzing the numbers between the digits given:

Now between $999$ and $10000$ we have all four digit numbers and we need to find the numbers formed with the help of $0,2,3,6,7,8$.

Evaluate the numbers starting with $0,2,3,6,7,8$ which lie between $999$ and $10000$.

Now $0$ will be removed because numbers starting from $0$ will be three digit number and will not lie between $999$ and $10000$.

So $0$ cannot be placed at thousands place.

So total numbers of ways of forming four digit number by keeping

$2$ at thousands place .$=5\times 4\times 3$

.$3$ at thousands place .$=5\times 4\times 3$

$6$ at thousands place .$=5\times 4\times 3$

$7$ at thousands place .$=5\times 4\times 3$

$8$ at thousands place .$=5\times 4\times 3$

.and so therefore we have $5$ ways of placing the numbers at thousand place ,

Therefore, total numbers formed $5\times \left(5\times 4\times 3\right)=300$

Hence, correct option is (C).