I have doubt in this question as we are arranging the letters and you mentioned order is not important . suppose, we are choosing minimum 15 then there might be two possibility for which the question holds true. i.e AB can also be placed as BA which gives 2 possibility and thus 2/105 which is not less than 1 percent.

If you treat AB and BA as two different pairs, then the base of 2/105 mentioned by you is actually 105 times 2 as A(2, 15) = 15*14 = 210 = 105 * 2. Then the answer will still be 2/210 = 1/105