Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?
Answers:
A) 2,145 B) 6,435 C) 12,100 D) 12,870 E) 25,740
Total 3 letter passwords = 26 * 25 * 24= 
<gadget id="calculator">26 * 25 * 24</gadget>
<output>15_600</output>
15600   Total letters= 26 = symmetrical letters (11) + asymmetrical letters (x) =&gt; x = 15   Total no. of 3 letters passwords using asymmetrical letters = 15 * 14 * 13= 
<gadget id="calculator">15 * 14 * 13</gadget>
<output>2_730</output>
2730 (no repetition allowed)   Hence, no. of 3 letter passwords using atleast one symmetrical letter= 15600 - 2730= 
<gadget id="calculator">15600 - 2730</gadget>
<output>12_870</output>
12870 ---&gt; Option 12,870
<result>D</result>
Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?