Question

How many four-letter computer passwords can be formed using only the symmetric letters (no repetition allowed)?

• A. 7,920
• B. 330
• C. 14,640
• D. 4,19,430
• A. 990
• B. 2,730
• C. 12,870
• D. 15,600

Answer 1

The Correct Option is A

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.

Answer 2

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.