Question 147378: Alan is jealous that his neighbor down the street has a very cool toy that he has been admiring for 20 years now. He decides to break in and steal it. He knows that the house is monitored by a security system that requires a 5digit pass code. He knows that it needs 2 digits and 3 letters. How many pass keys are there if no digits can be repeated?
Answer by vleith(2983)   (Show Source):
You can put this solution on YOUR website! Assuming the first two keys are digits and the last three are letters (that is, assuming we know in advance this is that case), then
The first key is digits - so Alan has 10 choices
The second key is digits, but can't be the same digit used on key 1. So 10-1=9
The third key is letters - 26 possibilities
The fourth key is letters - 26 possibilities
The fifth key is letters - 26 possibilities
So, 10*9*26*26*26 possible permutations
I never thought I would see a mathematics problem that appeals to a thief!
Next question, what is the probability Alan gets caught and goes to jail? :)
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