Let x and y be distinct integers where 1 ≤ x ≤ 25 and 1 ≤ y ≤ 25 . Then, the number of ways of choosing x and y , such that x + y is divisible by 5 , is _____ .

Step-by-step solution

Given: 1 ≤ x , y ≤ 25 And, x , y are distinct integers. Let x + y = 5 k , where k ∈ N So, we have x y Number of ways 5 λ i.e, 5 ,   10 ,   15 ,   20 ,   25 5 λ i.e, 5 ,   10 ,   15 ,   20 ,   25 Since, x and y are distinct integers, so we cannot pair 5 , 5 ,   10 , 10 , . . . 25 , 25 20 5 λ + 1 i.e., 1 ,   6 ,   11 ,   16 ,   21 5 λ + 4 i.e., 4 ,   9 ,   14 ,   19 ,   14 25 5 λ + 2 i.e, 2