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 ?

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Solution

There are three possible cases that will satisfy the condition of forming three letter towards with at let $1$ symmetric letter.

Case $1 : 1$ symmetric and $2$ asymmetric or

Case $2 : 2$ symmetric and $1$ asymmetric or

Case $3 :$ all $3$ symmetric

$= [(^{11} C_{1} \times^{15} C_{2}) + (^{11} C_{2} \times^{15} C_{1}) +^{11} C_{3}] \times 3!$

$= 12870$

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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 ?

There are three possible cases that will satisfy the condition of forming three letter towards with at let 1 symmetric letter.Case 1: 1 symmetric and 2 asymmetric orCase 2: 2 symmetric and 1 asymmetric orCase 3: all 3 symmetric=[(11C1×15C2)+(11C2×15C1)+ 11C3]×3!=12870

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 ?