Suppose we have 15 graphics cards and 4 servers. The graphics cards are all identical, but the servers are not and are numbered 1, 2, 3, 4. How many different ways can we allocate graphics cards to servers? Assume that a server can make use of any number of graphics cards, including 0. (Note: since servers are distinct but graphics cards are indistinguishable, moving a graphics card from server 1 to server 2 creates a new assignment, but swapping a graphics card in a given server with another identical graphics card doesn't.)

Question
Suppose we have 15 graphics cards and 4 servers. The graphics cards are all identical, but the servers are not and are numbered 1, 2, 3, 4. How many different ways can we
allocate graphics cards to servers? Assume that a server can make use of any number of graphics cards, including 0.
(Note: since servers are distinct but graphics cards are indistinguishable, moving a graphics card from server 1 to server 2 creates a new assignment, but swapping a graphics
card in a given server with another identical graphics card doesn't.)
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Suppose we have 15 graphics cards and 4 servers. The graphics cards are all identical, but the servers are not and are numbered 1, 2, 3, 4. How many different ways can we allocate graphics cards to servers? Assume that a server can make use of any number of graphics cards, including 0. (Note: since servers are distinct but graphics cards are indistinguishable, moving a graphics card from server 1 to server 2 creates a new assignment, but swapping a graphics card in a given server with another identical graphics card doesn't.)

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