Question

How many four digit different numbers, greater than 5000 can be formed with the digits 1,2,5,9,0 when repetition of digits is not allowed?

Answer 1

Since the required numbers are greater than 5000.
$\therefore$ The thousand's place can be filled with any of two digits 5 or 9.
So, there are 2 ways of filling the thousand's place.
Since repetition of digits is not allowed, so the hundred's ten's and one's places can be filled in 4,3 and 2 ways respectively.
Hence, the required number of numbers
=$2\times 4\times 3\times 2=48$