Let $S=\{0,1,2,3, \ldots, 100\}$. The number of ways of selecting $x, y \in S$ such that $x \neq y$ and…
Let $S=\{0,1,2,3, \ldots, 100\}$. The number of ways of selecting $x, y \in S$ such that $x \neq y$ and $x+y=100$ is
51
40
50
100
Solution
Let $S=\{0,1,2,3, \ldots, 100\} x, y \in s$.
and
$
x+y=100
$
If $x=0$,
$y=100$
$x=1$,
$y=99$
$x=49 \Rightarrow y=51$
In this way, the total pairs in 50 .
So, the number of required ways $=50$