Question

Let $x$ and $y$ be distinct integers where $1 \leq x \leq 25$ and $1 \leq y \leq 25$ Then, the number of ways of choosing $x$ and $y$, such that $x+y$ is divisible by 5 , is ____

Answer 1

The correct answer is 120
x+y=5λ
Cases :

x	y	**Number of ways **
5λ	5λ	20
5λ+1	5λ+4	25
5λ+2	5λ+3	25
5λ+3	5λ+2	25
5λ+4	5λ+1	25

$\therefore$ Total number of ways are 120