Four candidates are running for president of the student council. three other candidates are running for vice-president. how many different ways can the two offices be filled?
4 * 3 = ?
To find the number of different ways to fill the two offices, we can use the concept of combinations.
Step 1: Calculate the number of ways to choose the president.
Since there are four candidates running for the position of president and only one candidate can hold this position, there are 4 ways to choose the president.
Step 2: Calculate the number of ways to choose the vice-president.
Since there are three candidates running for the position of vice-president and only one candidate can hold this position, there are 3 ways to choose the vice-president.
Step 3: Multiply the number of ways to choose the president by the number of ways to choose the vice-president.
To count all the possible combinations, multiply the number of ways to choose the president (4) by the number of ways to choose the vice-president (3):
4 (president choices) * 3 (vice-president choices) = 12
Therefore, there are 12 different ways to fill the two offices of president and vice-president with the given candidates.