Question 624437
To make numbers greater than 41000 you need to use 4 or 5 for the first (then thousands place) digit. That is necessary and sufficient.
So you have {{{highlight(2)}}} choices for the first digit.
For either choice, you are left with 4 of the digits 1, 2, 3, 4, 5.
It does not matter which four are left (we could call them A, B, C, and D, or 1, 2, 3, and D), they can be arranged in {{{4*3*2*1=highlight(24)}}} ways.
(The permutations of 4 items taken 4 at a time is factorial of 4, and 4!= {{{4*3*2*1}}}=24).
So the total number of 5-digit combinations, with all different digits, that make a number greater than 41000 is
{{{2*24=highlight(48)}}}