Question: Grossman Combinatorics questions. (a) A program to generate all the permutations of a set is run on a computer that writes the output to a

Grossman Combinatorics questions.

(a) A program to generate all the permutations of a set is run on a computer that writes the output to a le at a rate of 1000 permutations per second. How long will it take the computer to generate all the permutations of a set with 16 elements?

(b) A computer network is secured by an alpha-numeric password consisting of exactly 9 characters. The rst and last characters of the password must be a letter, and the remaining characters may be a digit or a letter. (Assume that there are 26 di erent letters and that no distinction is made between upper-case and lower-case letters.) A password is valid if at least one of the characters is a digit. How many valid passwords are there?

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