Ummm... i dont know if im too late, and the answers already been worked out or whatever, but im gonna have a shot ne way. if its already been worked out or someones already tried this way and been proven wrong or i basically make a fool of myself in ne way (which i often seem to do on this thing... :/ ) then please ignore this!
Ok so here goes. If you take all the possible arrangements of the letters in BANANAS with A as the first letter like that other guy did (i didn't check it, i just counted it and he got ten, iincluding the one the girl added on so im just assuming thats right.) and then you multiply that by two (for all possible arrangements with A as the last letter) and then multiply THAT by 3! (for all possible arrangements of the three As) and then divide that by 420 (which is all of the possible arrangements of the letters in the word BANANAS: 7!/3!2!) well you then get 2/7, which thingo said was the answer so yeh. does that sound right?
(10 x 2 x 3!) / (7!/3!2!)