SOLUTION: Consider all four-digit numbers that can be formed each time taking the 4 digits of 2014. Without repeating any digit, what is the sum??

In thes problems always choose the most restrictive things first.

We can't choose the first digit as 0, so it's the mosty restrictive.

We can choose the first digit 3 ways {2,1,4}
We can choose the second digit as any of the 3 remaining ways. (it can be 0).
We can choose the second digit either of the 2 remaining ways.

That's 3*3*2 = 18 ways.

Here are all 18 ways:

 1. 1024
 2. 1042
 3. 1204
 4. 1240
 5. 1402
 6. 1420
 7. 2014
 8. 2041
 9. 2104
10. 2140
11. 2401
12. 2410
13. 4012
14. 4021
15. 4102
16. 4120
17. 4201
18. 4210

Edwin