How many 4 letter computer password can be formed using only the symmetric letter no repetition allowed?

1. How many three letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter ?

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   • How many four-letter computer passwords can be formed using only the symmetric letters (no repetition allowed)?$\left( {\text{A}} \right){\text{ 7920}}$$\left( {\text{B}} \right){\text{ 330}}$\[\left( {\text{C}} \right){\text{ 14640}}\]\[\left( {\text{D}} \right){\text{ 419430}}\]
   • How many 4 letter computer password can be formed using only the symmetric letters no repetition allowed?
   • How many ways five letter passwords can be created when letters can be repeated?

1. 1. 990
   2. 2730
   3. 12870
   4. 1560000

Correct Option: C

Total number of password using all alphabets -Total
number of password using no symmetric alphabets
= (26 x 25 x 24 ) - (15 x 14 x 13 )
= 12870

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Instructions

Directions for the next two questions: Answer the questions based on the following information.

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 four-letter computer passwords can be formed using only the symmetric letters (no repetition allowed)? <ul class="answers"> <li><div class="answernumber">A</div>$$7920$$</li> <li><div class="answernumber">B</div>$$330$$</li> <li><div class="answernumber">C</div>$$14640$$</li> <li><div class="answernumber">D</div>$$419430$$</li> </ul> <div class="clearfix"></div> <h4>Solution</h4> <div>In English alphabets $$11$$ letters are there which are symmetric.</div><div>So, total ways $$=11\times10\times9\times8$$</div><div>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $$=7920$$</div><div>Hence, the answer is $$7920.$$<br></div><div><br> </div> </div> </div> </div> <script src="https://www.getpractice.com/public/jquery.js">

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