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Use P (n, r) and/or C(n, r) for your answers

(a) A website password requirements say the pasword must contain a sequence of 5 letters (A through Z) followed by 8 digits (0 through 9). How many passwords start with AXB and end with an even number?

(b) A quiz contains 55 questions. Suppose that for each question there are 4 possible answers to select from. In how many different ways can the quiz be completed if all the

questions in it are answered?

(c ) There are 30 different encyclopedia, among which 15 are history encyclopedias, 5 are geology encyclopedias, and 10 aremath encyclopedias. In how many different ways can the 30 encyclopedias be arranged in a row if the first 15 encyclopedias are history, the next 5 are geology books, and the last 10 books are math?

(d) A highschool student board consists of 10 members to be selected from a pool of 15 seniors and 20 freshmen. In how many different ways can such a student board be formed if it must contain at least one freshman?

SOLUTION :- Your solution is given below.

(a). For counting the number of passwords that start with ...