Each of the letters A, H, I, M, O, T, U, V, W, X, Y appears same when looked at

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Each of the letters A, H, I, M, O, T, U, V, W, X, Y appears same when looked at in the mirror. (No lateral inversion). They are hence called symmetric letters. Other letters in the alphabet are asymmetric letters. How many 4 letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?

Options:

A . 11770

B . 12540

C . 326040

D . 13585

Answer: Option C
:
C
Method 1
There are four possible cases that satisfy the condition of forming 4-letter passwords with at least one symmetric letter.
Case 1: 1 symmetric letter + 3 unsymmetric letters
Case 2: 2 symmetric letters + 2 unsymmetric letters
Case 3: 3 symmetric letters + 1 unsymmetric letter
Case 4: All 4 symmetric letters
= {(

^{11}

C

_{1}

\times

^{15}

C

_{3}

) + (

^{11}

C

_{2}

\times

^{15}

C

_{2}

) + (

^{11}

C

_{3}

\times

^{15}

C

_{1}

) + (

^{11}

C

_{4}

) }
=5005 + 5775 + 2475 + 330
=13585

\times

4! = 326040
Method 2
Total number of cases- cases where there are no symmetric letters

^{26}

C

_{4}

-

^{15}

C

_{4}

= 13585

\times

4! = 326040

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