Math Problem Statement
Suppose a password based authentication system requires the password to be 15 characters long and it should contain exactly two digits, exactly two of the six special characters, namely, {!, @, #, $, %, &} and the rest of the characters can be upper and lower case letters. How many such passwords are possible?
Solution
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Probability
Permutations and Combinations
Exponential Functions
Formulas
Combination formula: C(n, k) = n! / (k! * (n - k)!)
Permutation formula: P(n, k) = n! / (n - k)!
Exponential function: a^b
Theorems
Basic counting principle
Suitable Grade Level
Grades 11-12
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