Let n1 < n2 < n3 < n4 < n5 be positive integers such that n1 + n2 + n3 + n4 + n5 = 20. Then the number of such distinct arrangements (n1, n2, n3, n4, n5) is?

When n5 takes value from 10 to 6 the carry forward moves from 0 to 4 which can be arranged in 4C0 + 4C1 + 4C2 + 4C3 + 4C4 = 1 + 4 + 6 + 4 + 1 = 16
Alternate solution
Possible solutions are
1,2,3,4,10
1,2,3,5,9
1,2,3,6,8
1,2,4,5,8
1,2,4,6,7
1,3,4,5,7
2,3,4,5,6
Hence, there are 7 solutions.