Question

The Greater Knightrola Small Monster Association has four chartered positions: President, Vice President, Treasurer and Secretary; it also has 12 officers chosen at large. All of these seats must be filled by members of GKSMA, of which there are 50. No member may hold more than 1 position. How many different ways are there to fill the positions? (Note: Two ways are considered different if there is a person in one way who has a different role or no role in the other way. For example, if Alice is President in one way and she is Vice President in another, those two ways must count differently. But if she is an at large member in both ways, that is not by itself enough for those ways to be different.

Answer 1

There are 500,278,636,895,125,000,000 different ways to fill the positions of the Greater Knightrola Small Monster Association.

Step-by-step explanation:

To find the number of different ways to fill the positions of the Greater Knightrola Small Monster Association, we need to consider the different possibilities for each position.

1. President: There are 50 members to choose from, so there are 50 choices for the President position.

2. Vice President: After the President is chosen, there are 49 members remaining to choose from for the Vice President position.

3. Treasurer: After the President and Vice President are chosen, there are 48 members remaining to choose from for the Treasurer position.

4. Secretary: After the President, Vice President, and Treasurer are chosen, there are 47 members remaining to choose from for the Secretary position.

5. Officers at large: There are 12 positions to fill, and each position can be filled by any of the 50 members. Therefore, the number of ways to fill the officer positions is 50 choices for the first position, multiplied by 50 choices for the second position, and so on, for a total of 50^12 (using the multiplication principle).

To find the total number of ways to fill all the positions, we multiply the number of choices for each position together: 50 * 49 * 48 * 47 * (50^12).

Therefore, there are a total of 500,278,636,895,125,000,000 different ways to fill the positions of the Greater Knightrola Small Monster Association.