How many distinguishable ways are there to write 9 as the sum of 1's, 3's and 4's, where the order of the addends matters? For example, 1 + 3 + 4 + 1 and 4 + 1 + 3 + 1 are two different ways.
4 + 4 + 1 = 9.............................3permutations
4 + 3 + 1 + 1 = 9........................12p
4 + 1 + 1 + 1 + 1 + 1 = 9.............6p
3 + 3 + 3 = 9...............................1p
3 + 3 + 1 + 1 + 1 = 9....................10p
3 + 1 + 1 + 1 + 1 + 1 + 1 = 9.........7p
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 9..1p
Total permutations ==40 - ways
