The number 4 can be expressed as the sum of one or more natural numbers in eight different ways if order matters:
| 4 | 1+3 | 2+2 | 3+1 | 1+1+2 | 1+2+1 | 2+1+1 | 1+1+1+1 |
How many expressions are there for the number 7?
7 = 7...........................................1
6 + 1 = 7.....................................2
5 + 2 = 7.....................................2
5 + 1 + 1 = 7...............................3
4 + 3 = 7.....................................2
4 + 2 + 1 = 7...............................6
4 + 1 + 1 + 1 = 7.........................4
3 + 3 + 1 = 7...............................3
3 + 2 + 2 = 7...............................3
3 + 2 + 1 + 1 = 7........................12
3 + 1 + 1 + 1 + 1 = 7...................5
2 + 2 + 2 + 1 = 7.........................4.
2 + 2 + 1 + 1 + 1 = 7..................10
2 + 1 + 1 + 1 + 1 + 1 = 7.............6
1 + 1 + 1 + 1 + 1 + 1 + 1 = 7.......1
Total =64 arrangements.
