Question

How many ways can the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members?

1) permutation; 28P4 = 491,400
2) permutation; 24P4 = 255,024
3) combination; 28C4 = 20,475
4) combination; 24C4 = 10,626

Answer 1

The number of ways to fill four specific offices from a club with 28 members is a permutation problem, and the correct answer is 491,400 ways, which is calculated as 28P4 or 28 x 27 x 26 x 25.

Step-by-step explanation:

The question pertains to the number of ways to fill four specific offices from a club with 28 members.

This is a permutation problem because the order in which the members are chosen matters; the roles of chairman, vice chairman, secretary, and treasurer are distinct.

To solve this, we would use the permutation formula, which in this case is 28P4. The correct permutation can be calculated as follows:

1. Select a chairman from the 28 members (28 options).
2. Select a vice chairman from the remaining 27 members (27 options).
3. Select a secretary from the remaining 26 members (26 options).
4. Select a treasurer from the remaining 25 members (25 options).

The total number of permutations is 28 x 27 x 26 x 25, which equals 491,400. So the correct answer is option 1) permutation; 28P4 = 491,400.