Finding the marginal distribution for problem with n balls. I am trying to solve the following problem:

A box contains N balls: $N_1\ white, N_2\ black,\ and\ N_3\ red\ (N = N_1 + N_2 + N_3).$ A random sample
  of n balls is selected from the box (without replacement). Let $Y_1, Y_2, and\ Y_3$ denote the number of white, black, and red balls, respectively, observed in the sample. Define $c = (N − n)/(N − 1)$, and
  $p_i = N_i/N,\ for\ i = 1, 2, 3.$  Assume $3 ≤ n ≤ min{\{N_1, N_2, N_3}\}$.
How to deduce the marginal distributions of $Y_1, Y_2, and\ Y_3,$ and compute their respective means and variances.and find their $Cov(Y_1, Y_2)$. and $Y_i \sim Hypergeometry(N,N_i,n)$. 

Also $Cov(Y_1,Y_2)= E(Y_1Y_2)-E(Y_1)E(Y_2)$. But How could I find $E(Y_1Y_2)$?
Any suggestion or help would be highly appreciated. 

Consider $Y_1+Y_2 \sim Hypergeometric(N,n,N_1+N_2)$ to find $Var(Y_1+Y_2)$.
Then use the identity,
$Var(Y_1+Y_2)=Var(Y_1)+Var(Y_2)+2Cov(Y_1,Y_2)$
