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 c…

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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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