Question 1206447
<pre>

Consider putting A in one on those first 4 spaces and
B somewhere to the right of it.

_C_D_E_F_ 

Successful ways:
We can pick a letter to put A immediately before and B immediately after
in 4 ways.

_C_D_E_F_

Possible ways:
We can choose a pair of spaces from the 5 to put A in the leftmost one 
and B in the rightmost one in C(5,2) = 10 ways.

The probability is 4/10 or 2/5.  The ratio is the same for any arrangement
of CDEF, and either arrangement of AB, so that's the final answer. 

[If we like we could multiply numerator and denominator by the 4! ways to
arrange CDEF and also by 2! for the 2 arrangements of AB, but why bother?
The ratio, i.e., the probability, would be the same.]

Edwin</pre>