On Jan 8, 8:37*pm, Jerry W. Lewis wrote:
I agree that modern computer exection time is quite fast, but for me the real
issue would be the time required to program and validate a routine that would
run through all the combinations. *That is the beauty of the generating
function approach.

Yes, stick with what you do best.

As for the program development time: as I said, 5-10 minutes.
Validation comes from scaling down to a tractable problem that can be
solved easily by hand. That was the lion's share of the 5+ minutes.
As trivial as the programming seems to be, I like to step through or
add debug prints to be sure that everything is copacetic. As it turns
out, my only error was in my "hand" calculations -- probably a typo on
the calculator.

But I agree that a mathematical solution often provides greater
insight.

My real point was: the OP might consider a programming solution that
does indeed enumerate all combinations exhaustively, if that is
acceptable and easier for him/her. You dismissed the possibility
based on incorrect presumptions ("exceptionally tedious and time-
consuming").