Eight first class and six second class petty officers are on the board of the 56 club. Inhow 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 officersand the vice-president and treasurer must be second class petty officers?

Eight first class and six second class petty officers are on the board of the 56 club. Inhow 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 officersand the vice-president and treasurer must be second class petty officers? Correct Answer 1680

Since two of the eight first class petty officers are to fill two different offices, we write 8P2=56

Then, two of the six second class petty officers are to fill two different offices; thus, we write 6P2 =30

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