The number of ways of selecting two numbers \(a\) and \(b, a\) \(\in\{2,4,6, \ldots ., 100\}\) and \(b \in\{1,3,5, \ldot…

The number of ways of selecting two numbers \(a\) and \(b, a\) \(\in\{2,4,6, \ldots ., 100\}\) and \(b \in\{1,3,5, \ldots ., 99\}\) such that 2 is the remainder when \(a+b\) is divided by 23 is