Question 388015: i want some very difficult questions in permutations and Combinations with the solutions and explanations >>> please
Answer by mdenny(8)   (Show Source):
You can put this solution on YOUR website! 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?
Explanatory Answer:
There are three possible cases that will satisfy the condition of forming three letter passwords with at least 1 symmteric letter.
Case 1: 1 symmetric and 2 asymmetric or
Case 2: 2 symmetric and 1 asymmetric or
Case 3: all 3 symmetric
= {(11c1 * 15c2) + (11c2 * 15c1) + 11c3} * 3!
= {11* + * 15 + } x 6
= {1155 + 825 + 165} * 6
= 2145 * 6 = 1287O
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