Can anyone help me out with this command that I am trying to get to work:

Sum[((Binomial[12, i]*Binomial[40, n - i])/Binomial[52, n]), {i, 1, n}] /. n -> {1, 2, 3, 4}

I would like it to carry out the sum four times and return the results for each one. If I go in and manually change the n on the top of the sum for each of the desired values, it works fine... however that defeats the purpose of using the /.

Thanks in advance.