If the number of solutions of the equation x + y + z = 20 , where 1 ≤ x < y < z and x , y , z ∈ I is k , then k 10 is equal to

Step-by-step solution

Let, y = x + h , where h &#8805; 1 and z = x + h + k , where k &#8805; 1 . Then, x + y + z = 20 &#8658; x + x + h + x + h + k = 20 &#8658; 3 x + 2 h + k = 20 . When x = 1 &#8658; 2 h + k = 17 , then there are 8 ways. When x = 2 &#8658; 2 h + k = 14 , then there are 6 ways. When x = 3 &#8658; 2 h + k = 11 , then there are 5 ways. When x = 4 &#8658; 2 h + k = 8 , then there are 3 ways. When x = 5 &#8658; 2 h + k = 5 , then there are 2 ways. When x &#62; 5 &#8658; not possible. &#8658; Total number of ways = 24