pr.probability - Density function for a multivariate Bernoulli-like distribution

I'm looking for a distribution to model a vector of $k$ binary random variables, $X_1, ldots, X_k$. Suppose I have observed that $sum_i X_i = n$. In this case I do not want to treat them as independent Bernoulli random variables. Instead, I would like something like the multinomial:

$P(X_1=x_1, ldots, X_k=x_k) = f(x_1, ldots, x_k; n, p_1, ldots, p_k) = frac{n!}{x_1! cdots x_k!} prod_{i=1}^k p_i^{x_i}$

but instead of the $x_i$ being nonnegative integers, I want them restricted to be either 0 or 1. I have been trying to see if the multivariate hypergeometric is appropriate, but I'm not sure.

Thanks in advance for any advice.