Working with Binary numbers BASE(..., 2, 7) and bit operations BITXOR, BITAND

PeterBartholomew1 

I've used BITXOR and BITAND very sparingly and I've played with BITLSHIFT and BITRSHIFT.  I understand what the functions do but have not used them enough to the point where I can conceptualize a solution for combinations/permutations.  I'll study your solution provided to see where I can find ways to make use of these functions.

My current way of tackling this task is with the help of DEC2BIN.  I understand the limitations involved but for 127 possibilities it's more than up to the task (for much more than 127 perhaps Python is the best option.)

'GenerateCombinations
=LAMBDA(party,seats,combinations,LET(
    header, HSTACK(TOROW(party), "Seats"),
    n, COUNT(seats),
    seq, SEQUENCE(n),
    combinations, SUM(COMBIN(n, seq)),
    BIN_vector, DEC2BIN(SEQUENCE(combinations), n),
    height, ROWS(BIN_vector),
    GetSeats, LAMBDA(r, c,
        LET(
            bin_val, MID(INDEX(BIN_vector, r), c, 1),
            seat_total, INDEX(seats, c),
            bin_val * seat_total
        )
    ),
    SeatMatrix, MAKEARRAY(height, n, GetSeats),
    CoalitionSeats, BYROW(SeatMatrix, SUM),
    CoalitionMatrix, FILTER(HSTACK(SeatMatrix, CoalitionSeats), CoalitionSeats >= required),
    Results, SORT(CoalitionMatrix, n + 1),
    VSTACK(header, Results)
))