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Eight first class and six second class petty officers are on the board of the 56 club. In how many ways can the members elect, from the board, a president, a vice-president, a secretary, and a treasurer if the president and secretary must be first class petty officers and the vice-president and treasurer must be second class petty officers?

Correct Answer: 1680

Explanation:

Since two of the eight first class petty officers are to fill two different offices, we write 8 P 2 = 56


 


Then, two of the six second class petty officers are to fill two different offices; thus, we write  6 P 2  =30


 


The principle of choice holds in this case; therefore, the members have 56 x 30 = 1680 ways to select the required office holders


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