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A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 15 members and any member can be elected

to each position? no person can hold more than one position.
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1 Answer

This is a permutation problem.  There are 15 different possibilities for the president.  Once the president is selected, there are now only 14 different possibilities for vice-president.  And once the vice-president is selected, there are only 13 different possibilities for the secretary-treasurer.  So it is:

15 * 14 * 13 = 2730