SOLUTION: How many different ways can class officers be selected if there are three candidates for President, four candidates for Vice President, and seven candidates for Secretary?

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I am assuming that no one is running for two or three different positions at the same time.
The choices for the three positions are independent.
There are 3 ways to chose the President.
For each one of those choices, you still have four different ways to choose a Vice President.
That gives you ways to chose President plus Vice President.
For each of those 12 choices, you still have 7 ways to choose a secretary,
so there are ways to chose the set of 3 class officers.