Boolean vectors of length $6$ formed by exactly three zero's and three one's

Question

The boolean vectors formed by exactly three zero's and three one's are

$\binom{6}{3}\binom{6}{3}=400$

Is it wrong?

Answer 1

Yes, it is wrong. Once you choose which three of the $6$ positions are $0$, the other three must be $1$.

Answer 2

Hint: After you have chosen $3$ spots for the 0's, is there really anything more left to choose?