If $^{n} C_{x} =^{n} C_{y}$ , then x+y $=$

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Solution

Given
${^{n} C}_{x} = {^{n} C}_{y} . . . . . . . . (1)$
We Know that
${^{n} C}_{r} = {^{n} C}_{n - r} . . . . . . . . (2)$
Comparing (1) and (2)
$r = x n - r = y$
Now ,
$x + y = r + n - r = n \Rightarrow x + y = n$
Hence the value of $x + y = n$

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