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combinations with at least two different objects


New member
Oct 28, 2009
How can I calculate the number of combinations that differ by at least two objects? (order not important, no repetition allowed)
For (n=7, r=4) (a,b,c,d,e,f,g) we would get 35 combinations:
{a,b,c,d} {a,b,c,e} {a,b,c,f} {a,b,c,g} {a,b,d,e} {a,b,d,f} {a,b,d,g} {a,b,e,f} {a,b,e,g} {a,b,f,g} {a,c,d,e} {a,c,d,f} {a,c,d,g} {a,c,e,f} {a,c,e,g} {a,c,f,g} {a,d,e,f} {a,d,e,g} {a,d,f,g} {a,e,f,g} {b,c,d,e} {b,c,d,f} {b,c,d,g} {b,c,e,f} {b,c,e,g} {b,c,f,g} {b,d,e,f} {b,d,e,g} {b,d,f,g} {b,e,f,g} {c,d,e,f} {c,d,e,g} {c,d,f,g} {c,e,f,g} {d,e,f,g}

however, if we only want those that differ by at least two objects from all the other combinations, we'd end up with 7:
{a,b,c,d} {a,b,e,f} {a,c,e,g} {a,d,f,g} {b,c,f,g} {b,d,e,g} {c,d,e,f}

What is the formula for this?
Thanks a lot for your help,