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23 Sep 2009, 18:59
Kudos
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N
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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 three letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?
A. 2145
B. 12870
C. 6435
D. 12100
E. 25740
A. 2145
B. 12870
C. 6435
D. 12100
E. 25740
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23 Sep 2009, 20:19
Kudos
Bookmarks
The answer is B: 12870..
There are a total of 11 symmetric letters, and therefore, 15 asymmetric letters.
Total number of words possible (no repetition):
26*25*24 = 650*24 = 15600
Total number of words possible with only asymmetric letters:
15*14*13 = 210*13 = 2730
Total number of words with at least one symmetric letter:
15600 - 2730 = 12870
There are a total of 11 symmetric letters, and therefore, 15 asymmetric letters.
Total number of words possible (no repetition):
26*25*24 = 650*24 = 15600
Total number of words possible with only asymmetric letters:
15*14*13 = 210*13 = 2730
Total number of words with at least one symmetric letter:
15600 - 2730 = 12870
24 Sep 2009, 03:58
Kudos
Bookmarks
Kudos AK, elegant and simple! Permutations and combinations are my weaker part and you do help me here a lot.
I approached from the usual side:
1) Combinations of types of letters:
AAA - 1
AAS - 3 (3C2 = 3)
SSA - 3 (3C2 = 3)
2) Permutations within each combination
AAA = 11 x 10 x 9 = 990
AAS = 15 x 14 x 11 = 2310
SSA = 11 x 10 X 15 = 1650
3) Multiply by number of combinations and add those
990 + 2310 x 3 + 1650 x 3 = 12 870
I approached from the usual side:
1) Combinations of types of letters:
AAA - 1
AAS - 3 (3C2 = 3)
SSA - 3 (3C2 = 3)
2) Permutations within each combination
AAA = 11 x 10 x 9 = 990
AAS = 15 x 14 x 11 = 2310
SSA = 11 x 10 X 15 = 1650
3) Multiply by number of combinations and add those
990 + 2310 x 3 + 1650 x 3 = 12 870
