BooleanCountingFunction[{3, 6}, {a, b, c, d, e, f}]
BooleanCountingFunction[{3, 6}, {a, b, c, d, e, f}]; BooleanTable[%]
BooleanCountingFunction[{3, 6}, {a, b, c, d, e, f}]; BooleanTable[%]; Boole[%]