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.