Digital doubt

Question

Answer 1

$Y = A_1 \oplus B_1 \oplus A_2 \oplus B_2 \oplus A_3 \oplus B_3$

We know output of consecutive XOR is $1$ for odd no. of $1's$. So, for $Y$ to be $1$ odd number of variables out of $ A_1, B_1, A_2,  B_2, A_3, B_3$ should be $1$.

So, either $1$ variable should be $1$ (or) $3$ variables should be $1$ (or) $5$ variables should be $1$.

So, total combinations for $Y= 1$ are $\color{navy}{ \binom 6 1 + \binom 6 3 + \binom 6 5 = 6 +20 + 6 = 32}$