Let S = 0 , 1 , 2 , 3 , … , 100 . The number of ways of selecting x , y ∈ S such that x ≠ y and x + y = 100 is

Step-by-step solution

Given: S = 0 , 1 , 2 , 3 , … , 100 Now, possible ordered pair x ,   y ∈ S such that x ≠ y   &   x + y = 100 are 0 ,   100 ,   1 ,   99 ,   2 ,   98 ,   3 ,   97 , . . . . . . ,   48 ,   52 ,   49 ,   51 Therefore, total number of ways of selecting such pairs is 50 .