The number of integers, between 100 and 1000 having the sum of their digits equals to 14 , is _________

Step-by-step solution

N = ab c (i) aligned & All distinct digits & a + b + c =14 & a 1 & ~b , c 0 to 9 aligned array lll by hit & trial : & 8 cases (6,5,3) & (8,6,0) & (9,4,1) (7,6,1) & (8,5,1) & (9,3,2) (7,5,2) & (8,4,2) & (7,4,3) & (9,5,0) & array (ii) 2 same, 1 diff a=b ;c 2 a + c =14 by values : aligned & . array l (3,8) (4,6) (5,4) (6,2) (7,0) array 3 ! 2 ! 5-1 & =14 cases aligned (iii) all same : aligned & array l 3 a=14 a= 14 3 rejected 0 cases array aligned Hence, Total cases: aligned & 8 3 !+2 (4)+14 & =48+22 & =70 aligned