Question

How many 5 digit numbers can be formed from the digits 0, 1, 3, 7, 9 without repetition which are greater than 40000?

• A. $120$
• B. $96$
• C. $48$
• D. None of the above

Answer 1

The correct option is C $48$

Given digits: $0,1,3,7,9$

Since, the number formed has to be greater than $40000$

$\therefore$ First place can be filled by $2$ ways: $7$ or $9$

Second place be filled by $4$ ways: any remaining $4$ numbers.

Third place can be filled by $3$ ways: any remaining $3$ numbers

Fourth place can be filled by $2$ ways: any remaining $2$ numbers.

Fifth place can be filled by $1$ ways: last number remaining


$\therefore$ Total number of $5$ digits number greater than $40000$ $=2\times 4\times 3\times 2\times 1=48$