Mathematics - Permutation Combination Question with Solution | TestHub

When$n_5$takes value from 10 to 6 the carry forward moves from 0 to 4 which can be arranged in${}^4{C}_0+\frac{{}^4{C}_1}{4}+\frac{{}^4{C}_2}{2}+\frac{{}^4{C}_4}{1}=7$
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 7 solutions are there.