Final answer:
The election of officers for the Social Action club is a permutation because the order of selection matters as each role is distinct. The total number of ways to elect the president, vice president, secretary, and public relations officer from 15 members is the product of the choices as each position is filled, resulting in 15 x 14 x 13 x 12 possible ways.
Step-by-step explanation:
The question at hand involves determining whether the situation of electing officers for the Social Action club is an example of a permutation or a combination and subsequently calculating the number of different ways the officers can be elected. In this case, the order matters because the roles of president, vice president, secretary, and public relations officer are distinct positions. Therefore, it is a permutation situation.
To find the number of ways to elect the four officers from the 15 members, we must calculate the product of the available choices for each position as the roles are filled one by one. This is given by 15 choices for the president, then 14 for the vice president (after the president has been selected), 13 choices for the secretary, and finally 12 choices for the public relations officer.
The calculation would be as follows:
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- President: 15 ways
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- Vice President: 14 ways (after President is chosen)
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- Secretary: 13 ways (after President and Vice President are chosen)
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- Public Relations Officer: 12 ways (after President, Vice President, and Secretary are chosen)
Thus, the total number of ways to elect the officers is 15 x 14 x 13 x 12, which is option b).