Comprehension
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.
Question: 1
How many four-letter computer passwords can be formed using only the symmetric letters (no repetition allowed)?
How many four-letter computer passwords can be formed using only the symmetric letters (no repetition allowed)?
Show Hint
For problems involving no repetition, multiply the number of choices available for each letter.
Updated On: Aug 4, 2025
- 7,920
- 330
- 14,640
- 4,19,430
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The Correct Option is A
Solution and Explanation
The symmetric letters are A, H, I, M, O, T, U, V, W, X, Z, which gives a total of 11 symmetric letters.
We need to form a four-letter password with no repetition allowed. The number of possible passwords is the number of ways to choose 4 letters from 11, and arrange them:
\[
\text{Total passwords} = 11 \times 10 \times 9 \times 8 = 7,920.
\]
Thus, the Correct Answer is 7,920.
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Question: 2
How many three-letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?
How many three-letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?
Show Hint
Use the total possible passwords minus those without the required condition to find the number with the condition.
Updated On: Aug 4, 2025
- 990
- 2,730
- 12,870
- 15,600
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The Correct Option is B
Solution and Explanation
We need to calculate the total number of three-letter passwords and subtract the number of passwords with no symmetric letters (as these are the ones with at least one symmetric letter).
- Total number of three-letter passwords (without any restrictions) is:
\[
26 \times 25 \times 24 = 15,600.
\]
- Total number of three-letter passwords with no symmetric letters (using only the 15 asymmetric letters):
\[
15 \times 14 \times 13 = 2,730.
\]
- The number of passwords with at least one symmetric letter is:
\[
15,600 - 2,730 = 12,870.
\]
Thus, the Correct Answer is 2,730.
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