Each group of nominations is its own competition for a spot at the academy.
Senator 1 nominates candidates 1 - 10 on a competitive slate, 1 gets in.
Senator 2 nominates candidates A, B, C, 2, D, F, G, 9, H, I, on a competitive slate, B gets in because A is the principal for Congressman AND B is a stronger/better/more desired candidate for West Point.
Congressman nominates candidates A, Z, Y, 2, X, W, V, U, T on a principal with numbered alternates, A gets in.
#2 is on every slate, but doesn't win any slate. They are likely a great QNS that needs to apply next year.
It gets even more complicated when you put in that H is coming out of the prep school and will get in, U and Z (with an LOA) are underrepresented minorities that are selected nationally. T is picked up for prep school at USMA. The RC really liked #2, so they offered them a chance for Civil Prep. And finally C, 5, 9, and W are recruited athletes with C making the cut as a top 100 national wait list candidate. And then right at the nomination deadline, 3 sends in a Presidential request, and they are selected off that list. Now multiply that across 435 congressional districts and 100 senators.
One nomination gets you a shot at admission. More help since they increase your chance; however, nothing is guaranteed.