""Mathematically, boy," he told himself, "if nobody else original comes along, they're bound to run out of arrangements someday. What then?" What indeed. This sort of arranging and rearranging was Decadence, but the exhaustion of all possible permutations and combinations was death. It scared Eigenvalue, sometimes. He would go in back and look at the set of dentures. Teeth and metals endure"
Thomas Pynchon
You should be able to find the number of ways of choosing an option from list \( A \) and an option from list \( B \). The AND rule is \[ n(A \text{ AND } B) = n(A)\times n(B). \]
2. You should be able to find the number of ways of choosing an option from list \( A \) or an option from list \( B \). The OR rule (when \( A \) and \( B \) are mutually exclusive) is \[ n(A \text{ OR } B) = n(A) + n(B). \]
3. You should be able to find the number of permutations of \( n \) items. The number of permutations of \( n \) items is \[ n!. \]
You should be able to find the number of ways of choosing \( r \) items from a list of \( n \) items. The number of combinations of \( r \) objects out of \( n \) (when order does not matter) is \[ {^nC_r} = \frac{n!}{r!(n-r)!}. \] The number of permutations of \( r \) objects out of \( n \) (when order does matter) is \[ {^nP_r} = \frac{n!}{(n-r)!}. \]
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