What are the 4 digit combinations of the numbers 0 through 9?

There are 10!/(4!(10-4)!) = 210 such combinations assuming no repeats are allowed:

{0, 1, 2, 3}, {0, 1, 2, 4}, {0, 1, 2, 5}, {0, 1, 2, 6}, {0, 1, 2, 7}, {0, 1, 2, 8}, {0, 1, 2, 9}, {0, 1, 3, 4}, {0, 1, 3, 5},

{0, 1, 3, 6}, {0, 1, 3, 7}, {0, 1, 3, 8}, {0, 1, 3, 9}, {0, 1, 4, 5}, {0, 1, 4, 6}, {0, 1, 4, 7}, {0, 1, 4, 8}, {0, 1, 4, 9},

{0, 1, 5, 6}, {0, 1, 5, 7}, {0, 1, 5, 8}, {0, 1, 5, 9}, {0, 1, 6, 7}, {0, 1, 6, 8}, {0, 1, 6, 9}, {0, 1, 7, 8}, {0, 1, 7, 9},

{0, 1, 8, 9}, {0, 2, 3, 4}, {0, 2, 3, 5}, {0, 2, 3, 6}, {0, 2, 3, 7}, {0, 2, 3, 8}, {0, 2, 3, 9}, {0, 2, 4, 5}, {0, 2, 4, 6},

{0, 2, 4, 7}, {0, 2, 4, 8}, {0, 2, 4, 9}, {0, 2, 5, 6}, {0, 2, 5, 7}, {0, 2, 5, 8}, {0, 2, 5, 9}, {0, 2, 6, 7}, {0, 2, 6, 8},

{0, 2, 6, 9}, {0, 2, 7, 8}, {0, 2, 7, 9}, {0, 2, 8, 9}, {0, 3, 4, 5}, {0, 3, 4, 6}, {0, 3, 4, 7}, {0, 3, 4, 8}, {0, 3, 4, 9},

{0, 3, 5, 6}, {0, 3, 5, 7}, {0, 3, 5, 8}, {0, 3, 5, 9}, {0, 3, 6, 7}, {0, 3, 6, 8}, {0, 3, 6, 9}, {0, 3, 7, 8}, {0, 3, 7, 9},

{0, 3, 8, 9}, {0, 4, 5, 6}, {0, 4, 5, 7}, {0, 4, 5, 8}, {0, 4, 5, 9}, {0, 4, 6, 7}, {0, 4, 6, 8}, {0, 4, 6, 9}, {0, 4, 7, 8},

{0, 4, 7, 9}, {0, 4, 8, 9}, {0, 5, 6, 7}, {0, 5, 6, 8}, {0, 5, 6, 9}, {0, 5, 7, 8}, {0, 5, 7, 9}, {0, 5, 8, 9}, {0, 6, 7, 8},

{0, 6, 7, 9}, {0, 6, 8, 9}, {0, 7, 8, 9}, {1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 3, 6}, {1, 2, 3, 7}, {1, 2, 3, 8}, {1, 2, 3, 9},

{1, 2, 4, 5}, {1, 2, 4, 6}, {1, 2, 4, 7}, {1, 2, 4, 8}, {1, 2, 4, 9}, {1, 2, 5, 6}, {1, 2, 5, 7}, {1, 2, 5, 8}, {1, 2, 5, 9},

{1,2, 6, 7}, {1, 2, 6, 8}, {1, 2, 6, 9}, {1, 2, 7, 8}, {1, 2, 7, 9}, {1, 2, 8, 9}, {1, 3, 4, 5}, {1, 3, 4, 6}, {1, 3, 4, 7},

{1, 3, 4, 8}, {1, 3, 4, 9}, {1, 3, 5, 6}, {1, 3, 5, 7}, {1, 3, 5, 8}, {1, 3, 5, 9}, {1, 3, 6, 7}, {1, 3, 6, 8}, {1, 3, 6, 9},

{1, 3, 7, 8}, {1, 3, 7, 9}, {1, 3, 8, 9}, {1, 4, 5, 6}, {1, 4, 5, 7}, {1, 4, 5, 8}, {1, 4, 5, 9}, {1, 4, 6, 7}, {1, 4, 6, 8},

{1, 4, 6, 9}, {1, 4, 7, 8}, {1, 4, 7, 9}, {1, 4, 8, 9}, {1, 5, 6, 7}, {1, 5, 6, 8}, {1, 5, 6, 9}, {1, 5, 7, 8}, {1, 5, 7, 9},

{1, 5, 8, 9}, {1, 6, 7, 8}, {1, 6, 7, 9}, {1, 6, 8, 9}, {1, 7, 8, 9}, {2, 3, 4, 5}, {2, 3, 4, 6}, {2, 3, 4, 7}, {2, 3, 4, 8},

{2, 3, 4, 9}, {2, 3, 5, 6}, {2, 3, 5, 7}, {2, 3, 5, 8}, {2, 3, 5, 9}, {2, 3, 6, 7}, {2, 3, 6, 8}, {2, 3, 6, 9}, {2, 3, 7, 8},

{2, 3, 7, 9}, {2, 3, 8, 9}, {2, 4, 5, 6}, {2, 4, 5, 7}, {2, 4, 5, 8}, {2, 4, 5, 9}, {2, 4, 6, 7}, {2, 4, 6, 8}, {2, 4, 6, 9},

{2, 4, 7, 8}, {2, 4, 7, 9}, {2, 4, 8, 9}, {2, 5, 6, 7}, {2, 5, 6, 8}, {2, 5, 6, 9}, {2, 5, 7, 8}, {2, 5, 7, 9}, {2, 5, 8, 9},

{2, 6, 7, 8}, {2, 6, 7, 9}, {2, 6, 8, 9}, {2, 7, 8, 9}, {3, 4, 5, 6}, {3, 4, 5, 7}, {3, 4, 5, 8}, {3, 4, 5, 9}, {3, 4, 6, 7},

{3, 4, 6, 8}, {3, 4, 6, 9}, {3, 4, 7, 8}, {3, 4, 7, 9}, {3, 4, 8, 9}, {3, 5, 6, 7}, {3, 5, 6, 8}, {3, 5, 6, 9}, {3, 5, 7, 8},

{3, 5, 7, 9}, {3, 5, 8, 9}, {3, 6, 7, 8}, {3, 6, 7, 9}, {3, 6, 8, 9}, {3, 7, 8, 9}, {4, 5, 6, 7}, {4, 5, 6, 8}, {4, 5, 6, 9},

{4, 5, 7, 8}, {4, 5, 7, 9}, {4, 5, 8, 9}, {4, 6, 7, 8}, {4, 6, 7, 9}, {4, 6, 8, 9}, {4, 7, 8, 9}, {5, 6, 7, 8}, {5, 6, 7, 9},

{5, 6, 8, 9}, {5, 7, 8, 9}, {6, 7, 8, 9}

If repeats are allowed, the number increases to 715 combinations

• I'll leave it as an exercise for the reader to list the extra 505

combinations.