A student council consists of 6 members, and 3 of them are officers (president, vice-president, and secretary). How many different ways are there to choose the officers, if each member can hold at most one office, and each office must be held by a different member?
Given that,
A student council consists of 6 members, and 3 of them are officers (president, vice-president, and secretary).
Since each member can hold at most one office.
The number of ways to choose the president is 6.
The number of ways to choose the vice president is 5 (since one member has already been chosen as the president).
The number of ways to choose the secretary is 4 (since two members have already been chosen as the president and vice president).
Thus, using the multiplication principle, the number of ways to choose the officers is:
Therefore, there are 120 different ways to choose the officers.
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