Let xyz be the three digit number x+y+z=10,x≤1,y≥0,z≥0 x−1=t⇒x=1+tx−1≥0,t≥0 t+y+z=10−1=90≤t,z,z≤9 ∴ Total number of non-negative integral solution =9+3−1C3−1=11C2=
11⋅10
2
=55 But for t=9,x=10, so required number of integers =55−1=54