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In a class of 22 students, the teacher calls on a student to give the answer to the first homework problem and then calls on a student to give the answer to the second homework problem. a. How many possible choices could the teacher have made if the same student was not called on twice? b. How many possible choices could the teacher have made if the same student may have been called on twice?

Stan has letter tiles AMTE. a. How many different ways can Stan arrange all four tiles? b. How many different arrangements begin with a vowel?

To duplicate a key, a locksmith begins with a dummy key that has several sections. The locksmith grinds a specific pattern into each section. a. A particular brand of house key includes 6 sections, and there are 4 possible patterns for each section. How many different house keys are possible? b. A desk key has 3 sections, and 64 different keys are possible. How many patterns are available for each section if each section has the same number of possible patterns?

A given region has the telephone prefix 472. a. How many 7-digit telephone numbers are possible with this prefix? b. How many of these possibilities end with 4 unique digits? c. How many of these possibilities form an even number?

Eli has homework assignments for 5 subjects but decides to complete 4 of them today and complete the fifth before class tomorrow. In how many different orders can he choose 4 of the 5 assignments to complete today?