Question

The number of positive integral solutions of x + y + z ≤ 10 is ..................

Answer 1

 Let  x + y + z + a = 10 

(where x ≥ 1, y ≥ 1,Z ≥1,a ∈ z&a  ≥ 0 )

Required number = ^{n + r – 1}C_r–1

= 7 + 4 - 1C_{4 - 1}  =  ¹⁰C₃

= 10.9.8/1.2.3 = 120