HCU MCA 2013 Paper

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Directions (Q. Nos. 14-15) Read the following information carefully to answer the questions that follow.
In the English alphabet there are 11 symmetric letters that appear the same when looked at in a mirror. Other 15 letters in the alphabet are asymmetric letters.

Question : 15 of 75

Marks: +1, -0

How many three letter computer passwords (no repetition allowed) can be formed with atleast one symmetric letter?

990
2145
12870
15600

Validate

Solution:

(b) Given, symmetric letters =11
and asymmetric letters = 15
∴ Required number of ways = Total number of three letter password - Three letter asymmetric password

\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;= ^ { 26 } { C } _ { 3 } - ^ { 15 } { C } _ { 3 }

\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;={26×25×24}/{3×2}-{15×14×13}/{3×2×1}

\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=2600-455

\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=2145

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