The letters of DRAFTY are arranged at random. What is the probability that the letters A and Y end up next to each other?
"DRAFTY" =6 letters =6! =720 permutations. Each permutation will begin with one of the 6 letters in: 720 / 6 = 120 ways. And so the letters "AY", in that order, will occur 120 times in the 720 permutations. Similarly, the letters "YA", in that order, will also occur 120 times in 720 permutation of the word "DRAFTY".
So, the probability of "A followed by Y, or "AY'' is: 120 /720 = 1/6
DRAFTY 6! arrangments just like guest said
Now tie the AY together. that could be AY or YA
Now you have 4 single letters and the double letter.
Prob that A and Y are next to each other = 2*5! / 6! = 2/6 = 1/3
which is the same as what guest got except I considered both AY and YA where guest only considered AY.