SOLUTION: Using the digits 1,2,3,4,5 only once .how many numbers greater than 41000 can be formed?

We can choose the first digit as 4, 5, or 6.  That's 3 ways.
We can choose the second digit as any of the remaining 4 ways.
We can choose the third digit as any of the remaining 3 ways.
We can choose the fourth digit as either of the remaining 2 ways.
We must choose the fifth digit as the only remaining 1 way.

Answer: 3·4·3·2·1 = 48 ways.

Edwin