There are a total of **11 symmetric letters**, and therefore, **15 asymmetric** letters.

**Method 1: **Total number of words possible (**no repetition**):

26*25*24 = 650*24 = 15600

Total number of words possible with **only asymmetric** letters:

15*14*13 = 210*13 = 2730

Total number of words with **at least one symmetric **letter:

15600 - 2730 = 12870

**Method 2 :**

**case1 :** Total combination possible with **1 symmetrical** and **2 asymmetrical** :

The symmetrical number can be in any one of the digits. So, totally 3 possibilities.

Hence, the total combination = 11* 15 * 14 * 3 = 6930

**case 2: **Total combination possible with** 2 symmetrical **and **1 asymmetrical :**

The asymmetrical number can be in any one of the digits. So, totally 3 possibilities.

Hence, the total combination = 11* 10 * 15 * 3 = 4950

**case 3: **Total combination possible with **3 symmetrical**:

All the letters symmetrical Hence, the total combination = 11* 10*9 = 990

Hence, total possible combination= 6930 + 4950 + 990 = 12870.

Hence,**(A)12870** is the Answer.