The defination of neutral function is those function which has equal number of Maxterm and minterm.
Now ,
We have $n$ variables so total number of combination possible is $2^{n}$.
No it will be a neutral function if output of half these combination is 1 and half of these combination is 0 which implies no of Maxterm is equal to no of minterm.
So we need half of the total combination means
$2^{n-1}$ is Maxterm and rest $2^{n-1}$ is minterm.
So this is same as selecting $2^{n-1}$ combination from total $2^{n}$ .
So with $n$ variable total number of neutral function is $\binom{2^{n}}{2^{n-1}}$
