Patrick D. Rockwell

2015-01-27 01:13:26 UTC

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Let's say that there are 2 men and 3 womenRaw Message

randomly entering a room one at time . You

want to make sure that the number of women

in the room is no more than 1.5 times the

number of men in the room. I've counted 2

ways that could happen. If you read from left

to right, that's the order in which they enter

the room.

MMWWW

MWMWW

Now let's try the same thing for with 4 men

and 6 women. I've counted 23 ways.

MMMMWWWWWW

MMMWMWWWWW

MMMWWMWWWW

MMMWWWMWWW

MMMWWWWMWW

MMWMMWWWWW

MMWMWMWWWW

MMWMWWMWWW

MMWMWWWMWW

MMWWMMWWWW

MMWWMWMWWW

MMWWMWWMWW

MMWWWMMWWW

MMWWWMWMWW

MWMMMWWWWW

MWMMWMWWWW

MWMMWWMWWW

MWMMWWWMWW

MWMWMMWWWW

MWMWMWMWWW

MWMWMWWMWW

MWMWWMMWWW

MWMWWMWMWW

Is there a way to calculate these numbers?

I've tried the fuss catalan formula and the

ballot theorem without success. Have I

miscounted?