Question 624437: Using the digits 1,2,3,4,5 only once .how many numbers greater than 41000 can be formed?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! 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  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  ways.
(The permutations of 4 items taken 4 at a time is factorial of 4, and 4!=  =24).
So the total number of 5-digit combinations, with all different digits, that make a number greater than 41000 is
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