Mellie.....others on this site (Melody, for instance) are better at these than I am.....but I'll venture an answer
I see all the white b***s as being indistiguishable from each other....and the same with the black b***s
So.....this amounts to the same thing as the number of identifiable "words" we could form with, say, 4 e's and 4 h's'
And this is given by 8! / (4! * 4!) = 70
There are only 2 ways to draw alternate colors .... BWBWBW.......etc. or WBWBWB......etc.
So.....the probability of alternating colors on the draws is just 2 / 70 or 1 / 35
If this isn't correct......maybe wait until Melody comes on later.....
