Applications
The theorem has many other interesting "non-marital" applications. For example, take a standard deck of cards, and deal them out into 13 piles of 4 cards each. Then, using the marriage theorem, we can show that it is always possible to select exactly 1 card from each pile, such that the 13 selected cards contain exactly one card of each rank (ace, 2, 3, ..., queen, king).
More abstractly, let G be a group, and H be a finite subgroup of G. Then the marriage theorem can be used to show that there is a set T such that T is an SDR for both the set of left cosets and right cosets of H in G.
The marriage theorem is used in the usual proofs of the fact that an (r × n) Latin rectangle can always be extended to an ((r+1) × n) Latin rectangle when r < n, and so, ultimately to a Latin square.
Read more about this topic: Hall's Marriage Theorem