How many ordered sets of positive integers are there if:

1.Their sum is less than** 6**

2. There are at most ** 4** addends

3. None of them is composite.

Please specify how quick were you to get the right answer.

(In reply to

re(2): Solution spoiler.....Now list them ALL! by Dej Mar)

There are two main kinds of set:

unordered sets, and ordered *sets*

An unordered set is just a list of numbers, for example; {1, 2, 3, 4, 5} is the set of natural counting numbers from 1 to 5. Mathematically, it wouldn't have made any difference if I had written {3, 1, 5, 2, 4} instead, since this is still the same set of numbers, regardless of the order I write them in.

In an ordered set, on the other hand; the order in which each number appears is important, and may even determine what each number in the set means. For example, if a point on a map has coordinates (10, 42), the number 10 might refer to the horizontal co-ordinate on the map, and then the number 42 would be the vertical co-ordinate on the map. If I swap the numbers and write (42, 10) instead; this is obviously a different place on the map.

The above (copied and pasted) relates to the answer provided by the solver:

the five sets {1,1}, {1,2}, {1,3}, {2,2}, {2,3}, actuallyimply

eight **ordered** sets {1,1}, {1,2}, {1,3}, {2,2}, {2,3},{2,1},{3,1},{3,2}, in similar way you should recount the triplets and the quadruplets.