Question

From a pool of 30 candidates, the offices of president, vice president, secretary, and treasurer will be filled. in how many different ways can the offices be filled?

Answer 1

To fill the offices of president, vice president, secretary, and treasurer from a pool of 30 candidates, there are 657,720 different ways the offices can be filled.

Step-by-step explanation:

To fill the offices of president, vice president, secretary, and treasurer from a pool of 30 candidates, we can use the concept of permutations. A permutation is an arrangement of objects where the order matters. In this case, the order in which the offices are filled matters. We have 30 choices for the president, then 29 choices for the vice president, then 28 choices for the secretary, and finally 27 choices for the treasurer. To find the total number of ways, we multiply these choices together:

1. 30 choices for president
2. 29 choices for vice president
3. 28 choices for secretary
4. 27 choices for treasurer

Therefore, there are 30 * 29 * 28 * 27 = 657,720 different ways the offices can be filled.

Answer 2

President is 1 of 30
Vice President is 1 of 29 left
Secretary is 1 of 28 left
Treasurer is 1 of 27 left

Total of different ways they can be filled = 30 * 29 * 28 * 27 = 657,720