Question

The digits $4,5,6,7$ and $8$ written in every possible order. The number of numbers greater than $56,000$ is

• A. $78$
• B. $72$
• C. $90$
• D. $88$

Answer 1

The correct option is C $90$

The number formed by the digits 4,5,6,7 and 8 which is greater than 56,000 is possible in two cases.

Case 1: let the ten thousand digit be greater than 5.

The possible numbers in this case are $=3\times 4\times 3\times 2\times 1=72$

Case 2: let the ten thousand digit number be 5 and the thousand digit number be either 6 or greater than 6.

So possible numbers in this case $3\times 3\times 2\times 1=18$

so total numbers = $90$