Grossman Combinatorics questions. (a) A program to generate all the permutations

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 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?

Explanation / Answer

Solution:

a) Total number of permutation is 20,922,789,888,000 .

Total Time = 20,922,789,888,000/1000 sec = 20,922,789,888 sec

b) Total Number of valid Password is = 26 * 36 * 36 *36*36*36*36*36*26- 26^9 =

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